Modul 11 - Analisis Big Data: Time Series Forecasting

Pengantar

Big Data: Big Data merujuk pada volume besar dan kompleks data yang tidak dapat secara efektif diolah atau dikelola menggunakan metode tradisional pemrosesan data. Data dalam skala besar ini seringkali berasal dari berbagai sumber, termasuk transaksi bisnis, media sosial, sensor IoT (Internet of Things), rekaman log, dan data lainnya. Big Data memiliki tiga karakteristik utama yang dikenal sebagai 3V: Volume (volume besar data), Variety (keragaman jenis data), dan Velocity (kecepatan pengumpulan dan pemrosesan data).

Tren Big Data di Masa Depan:

1. Peningkatan Penggunaan Kecerdasan Buatan (AI) dan Machine Learning (ML): Di masa depan, AI dan ML akan semakin mendominasi pengolahan dan analisis Big Data. Ini akan memungkinkan sistem untuk secara otomatis mengidentifikasi pola, tren, dan wawasan yang lebih dalam dari data berskala besar.

2. Integrasi Big Data dengan Internet of Things (IoT): Seiring dengan pertumbuhan IoT, akan ada integrasi yang lebih erat antara Big Data dan data yang dihasilkan oleh perangkat IoT. Ini akan memberikan pemahaman yang lebih baik tentang kinerja perangkat, pemantauan real-time, dan mendukung pengambilan keputusan yang lebih tepat waktu.

3. Keamanan dan Kepatuhan:

   • Keamanan Data yang Lebih Canggih: Dengan peningkatan ancaman keamanan, solusi keamanan data untuk melindungi informasi sensitif akan menjadi semakin canggih dan terintegrasi.
   • Kepatuhan Regulasi: Dengan meningkatnya regulasi terkait privasi data, organisasi akan semakin berfokus pada kepatuhan dan manajemen risiko untuk memastikan bahwa mereka mematuhi aturan dan peraturan yang berlaku.

4. Edge Computing untuk Pengolahan Data di Tempat: Seiring dengan peningkatan jumlah data yang dihasilkan oleh perangkat di edge devices, pengolahan data di tempat (edge computing) akan menjadi tren, mengurangi latensi dan memungkinkan pengambilan keputusan yang lebih cepat.

5. Penggunaan Quantum Computing: Meskipun masih dalam tahap pengembangan, quantum computing memiliki potensi untuk mengubah paradigma dalam pengolahan data berskala besar dengan memecahkan masalah yang sulit atau bahkan tidak dapat dipecahkan oleh komputer klasik.

6. Pengembangan Infrastruktur Big Data yang Lebih Efisien: Dengan meningkatnya kesadaran akan dampak lingkungan, akan ada peningkatan fokus pada pengembangan infrastruktur Big Data yang lebih efisien secara energi untuk mengurangi jejak karbon.

Tren-tren ini mencerminkan evolusi Big Data sebagai disiplin yang terus berkembang, memanfaatkan teknologi baru untuk memberikan wawasan yang lebih dalam dan memberdayakan organisasi untuk membuat keputusan yang lebih cerdas dan cepat.

Salah satu bentuk data yang termasuk ke dalam big data adalah Data Time Series

Data Time Series adalah data yang diperoleh dari pengamatan satu objek dari beberapa periode waktu. Misalnya data jumlah mahasiswa dari tahun ke tahun, data nilai tukar dolar terhadap rupiah dari hari ke hari, data kasus covid dari bulan januari 2020 sampai periode saat ini, dan masih banyak contoh yang lainnya.

Time series analysis adalah teknik statistik yang digunakan untuk menganalisis data yang dikumpulkan atau diukur secara berurutan selama periode waktu tertentu. Data time series mencakup observasi atau pengukuran yang dilakukan dalam interval waktu yang teratur. Contoh umum dari time series data termasuk data keuangan harian, data penjualan bulanan, atau data suhu harian.

Peran time series analysis dalam analisis big data sangat penting, terutama dalam konteks bisnis. Beberapa perannya melibatkan:

1. Prediksi dan Peramalan: Time series analysis memungkinkan perusahaan untuk membuat prediksi dan peramalan berdasarkan data historis. Misalnya, perusahaan dapat menggunakan analisis time series untuk memprediksi penjualan di masa depan, permintaan pelanggan, atau tren pasar.

2. Optimasi Keputusan: Dengan memahami pola dan tren dalam data time series, perusahaan dapat mengoptimalkan keputusan operasional. Ini mencakup penjadwalan produksi yang lebih baik, manajemen rantai pasokan yang efisien, atau penyesuaian harga yang tepat waktu, dan menetapkan strategi atau desain baru dari produk/service, atau rekomendasi produk baru, dll.

3. Deteksi Anomali: Time series analysis membantu dalam mendeteksi anomali atau perubahan yang tidak biasa dalam data. Ini dapat membantu perusahaan mengidentifikasi masalah operasional atau potensi risiko lebih awal, seperti gangguan produksi atau perubahan perilaku pelanggan yang tidak biasa.

4. Pengelolaan Inventori: Dengan memahami pola dalam data time series, perusahaan dapat mengelola inventori dengan lebih efisien, menghindari kekurangan atau kelebihan persediaan yang tidak perlu.

5. Optimasi Proses Bisnis: Analisis time series dapat digunakan untuk mengoptimalkan proses bisnis, seperti waktu produksi atau waktu pelayanan pelanggan, dengan memahami pola waktu tertentu yang mungkin mempengaruhi efisiensi.

Dengan memanfaatkan time series analysis dalam analisis big data, perusahaan dapat membuat keputusan yang lebih informasional, merencanakan strategi yang lebih baik, dan meningkatkan respons terhadap perubahan pasar atau keadaan bisnis.

Untuk melakukan analisis time series tersebut ada banyak teknik/metode/algoritma/model yang dapat digunakan, berikut beberapa diantaranya:

1. ARIMA, digunakan untuk tipe data stationary / random

2. ETS (error, trend, seasonal), sangat mirip pendekatannya dengan prophet facebook, yaitu dengan komponen trend dan seasonality

3. Bayesian Structural Time Series (BSTS), baik digunakan ketika ada eksternal regressor (atau pengaruh eksternal dari series lain selain komponen time series itu sendiri)

4. TBATS, model yang bisa digunakan ketika memodelkan “multiple seasonality” yaitu penggunaan 2 macam efek seasonality (misal weekly dan monthly), karena secara umum time series dianggap hanya memiliki 1 tipe seasonality

5. Prophet adalah model yang dikembangkan oleh Facebook dan fokus pada komponen: trend, seasonality (bisa multiple), dan holiday effect. dll.

Secara umum ada 3 komponen time series yaitu:

• Seasonal : data musiman, data dengan pola yang berulang dengan periode yang tetap (tahun, bulan, minggu, hari, jam, detik)

• Trend : ada 2 jenis trend yaitu cendrung naik atau cendrung turun

• Error : data yang ditangkap oleh Seosonal atau trend yang tidak bisa dijelaskan.

Load Packages

# Library untuk manipulasi data
library (dplyr)

## Warning: package 'dplyr' was built under R version 4.3.3

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# Library untuk visualisasi data
library (ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.3

library (plotly)

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

# Library model time series forecasting
library (prophet)

## Loading required package: Rcpp

## Loading required package: rlang

# Library untuk split data
library (caTools)

## Warning: package 'caTools' was built under R version 4.3.2

# Library manipulasi tanggal
library (lubridate)

## 
## Attaching package: 'lubridate'

## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union

Data Preparation

Import Data

sales <- read.csv("data/train.csv")
head(sales)

##         date store item sales
## 1 2013-01-01     1    1    13
## 2 2013-01-02     1    1    11
## 3 2013-01-03     1    1    14
## 4 2013-01-04     1    1    13
## 5 2013-01-05     1    1    10
## 6 2013-01-06     1    1    12

Melihat struktur data

# melihat struktur dataset
glimpse (sales)

## Rows: 730,500
## Columns: 4
## $ date  <chr> "2013-01-01", "2013-01-02", "2013-01-03", "2013-01-04", "2013-01…
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ item  <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ sales <int> 13, 11, 14, 13, 10, 12, 10, 9, 12, 9, 9, 7, 10, 12, 5, 7, 16, 7,…

Exploratory Data Analysis

Menampilkan transaksi berdasarkan store

group_sales <- group_by(sales, store)
count(group_sales)

## # A tibble: 10 × 2
## # Groups:   store [10]
##    store     n
##    <int> <int>
##  1     1 73050
##  2     2 73050
##  3     3 73050
##  4     4 73050
##  5     5 73050
##  6     6 73050
##  7     7 73050
##  8     8 73050
##  9     9 73050
## 10    10 73050

Bisa dilihat bahwa setiap store memiliki 73050 transaksi.

Menampilkan jumlah transaksi berdasarkan tanggal

Sekarang kita akan melihat jumlah transaksi berdasarkan tanggal transaksi dan kita simpan dalam objek daily_demand

daily_demand <- sales %>% 
  group_by(date) %>% 
  summarise( 
    demand=sum(sales)
  )  
daily_demand

## # A tibble: 1,461 × 2
##    date       demand
##    <chr>       <int>
##  1 2013-01-01  13696
##  2 2013-01-02  13678
##  3 2013-01-03  14488
##  4 2013-01-04  15677
##  5 2013-01-05  16237
##  6 2013-01-06  17291
##  7 2013-01-07  11769
##  8 2013-01-08  13560
##  9 2013-01-09  13878
## 10 2013-01-10  14642
## # ℹ 1,451 more rows

Menampilkan transaksi pada salah satu store

Kita akan mengambil transaksi pada salah satu store saja, misalnya pada store 3. dan kita simpan dalam objek daily_demandstore03 dan rubah data dateke type tanggal (date)

daily_demandstore03 <- sales %>% 
  filter (store == "3") %>%
  mutate (date = as.Date(date)) %>% #merubah type data date
  group_by(date) %>% 
  summarise( 
    demand=sum(sales)
  ) 
  
daily_demandstore03

## # A tibble: 1,461 × 2
##    date       demand
##    <date>      <int>
##  1 2013-01-01   1588
##  2 2013-01-02   1538
##  3 2013-01-03   1635
##  4 2013-01-04   1741
##  5 2013-01-05   1887
##  6 2013-01-06   1956
##  7 2013-01-07   1313
##  8 2013-01-08   1538
##  9 2013-01-09   1633
## 10 2013-01-10   1677
## # ℹ 1,451 more rows

Bisa dilihat bahwa data date sudah dalam type tanggal

Visualisasi Data

kita akan memvisualisasi trankasi pada store 03 dari tahun 2013 sampai 2016

plotstore03 <- daily_demandstore03 %>% 
  ggplot(aes(x = date, y = demand)) +
  geom_point(color = "tomato3", group=1) + 
  labs( 
    title = "Daily Sales", 
    subtitle = "Store 03", 
    caption = "1C Company", 
    x = "Date", 
    y = "Total Sales" 
  ) + 
  theme_minimal() 

ggplotly(plotstore03)

Membuat Objek Time Series dengan Model Prophet

Data yang digunakan yaitu data permintaan harian di Store 3 yang sudah disimpan pada objek daily_demandstore03

daily_demandstore03

## # A tibble: 1,461 × 2
##    date       demand
##    <date>      <int>
##  1 2013-01-01   1588
##  2 2013-01-02   1538
##  3 2013-01-03   1635
##  4 2013-01-04   1741
##  5 2013-01-05   1887
##  6 2013-01-06   1956
##  7 2013-01-07   1313
##  8 2013-01-08   1538
##  9 2013-01-09   1633
## 10 2013-01-10   1677
## # ℹ 1,451 more rows

Menyiapkan data

Untuk menggunakan algoritma/model Prophet pertama-tama yang harus dilakukan adalah menyiapkan data frame dengan format: ds untuk menyimpan tanggal, dan y untuk menyimpan dari nilai yang akan prediksi.

# Menyiapkan data
train_daily_3 <- daily_demandstore03 %>% 
  rename(
    ds = "date",
    y = "demand"
    )
glimpse(train_daily_3)

## Rows: 1,461
## Columns: 2
## $ ds <date> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0…
## $ y  <int> 1588, 1538, 1635, 1741, 1887, 1956, 1313, 1538, 1633, 1677, 1831, 1…

Fit Model Data Training

Melakukan pemodelan data training dengan menggunakan fungsi fit.prophet() dimana sebelumnya kita harus menentukan seasonality nya. dalam kasus ini kita mengggunakan daily.seasonality

# fitting model data training
model_ts <- prophet(daily.seasonality = TRUE, seasonality_prior_scale=0.1) %>% 
  fit.prophet(train_daily_3)
model_ts

## $growth
## [1] "linear"
## 
## $changepoints
##  [1] "2013-02-17 GMT" "2013-04-04 GMT" "2013-05-21 GMT" "2013-07-07 GMT"
##  [5] "2013-08-22 GMT" "2013-10-08 GMT" "2013-11-24 GMT" "2014-01-09 GMT"
##  [9] "2014-02-25 GMT" "2014-04-13 GMT" "2014-05-29 GMT" "2014-07-15 GMT"
## [13] "2014-08-31 GMT" "2014-10-17 GMT" "2014-12-02 GMT" "2015-01-18 GMT"
## [17] "2015-03-06 GMT" "2015-04-21 GMT" "2015-06-07 GMT" "2015-07-24 GMT"
## [21] "2015-09-08 GMT" "2015-10-25 GMT" "2015-12-11 GMT" "2016-01-26 GMT"
## [25] "2016-03-13 GMT"
## 
## $n.changepoints
## [1] 25
## 
## $changepoint.range
## [1] 0.8
## 
## $yearly.seasonality
## [1] "auto"
## 
## $weekly.seasonality
## [1] "auto"
## 
## $daily.seasonality
## [1] TRUE
## 
## $holidays
## NULL
## 
## $seasonality.mode
## [1] "additive"
## 
## $seasonality.prior.scale
## [1] 10
## 
## $changepoint.prior.scale
## [1] 0.05
## 
## $holidays.prior.scale
## [1] 10
## 
## $mcmc.samples
## [1] 0
## 
## $interval.width
## [1] 0.8
## 
## $uncertainty.samples
## [1] 1000
## 
## $specified.changepoints
## [1] FALSE
## 
## $start
## [1] "2013-01-01 GMT"
## 
## $y.scale
## [1] 5004
## 
## $logistic.floor
## [1] FALSE
## 
## $t.scale
## [1] 126144000
## 
## $changepoints.t
##  [1] 0.03219178 0.06369863 0.09589041 0.12808219 0.15958904 0.19178082
##  [7] 0.22397260 0.25547945 0.28767123 0.31986301 0.35136986 0.38356164
## [13] 0.41575342 0.44794521 0.47945205 0.51164384 0.54383562 0.57534247
## [19] 0.60753425 0.63972603 0.67123288 0.70342466 0.73561644 0.76712329
## [25] 0.79931507
## 
## $seasonalities
## $seasonalities$yearly
## $seasonalities$yearly$period
## [1] 365.25
## 
## $seasonalities$yearly$fourier.order
## [1] 10
## 
## $seasonalities$yearly$prior.scale
## [1] 10
## 
## $seasonalities$yearly$mode
## [1] "additive"
## 
## $seasonalities$yearly$condition.name
## NULL
## 
## 
## $seasonalities$weekly
## $seasonalities$weekly$period
## [1] 7
## 
## $seasonalities$weekly$fourier.order
## [1] 3
## 
## $seasonalities$weekly$prior.scale
## [1] 10
## 
## $seasonalities$weekly$mode
## [1] "additive"
## 
## $seasonalities$weekly$condition.name
## NULL
## 
## 
## $seasonalities$daily
## $seasonalities$daily$period
## [1] 1
## 
## $seasonalities$daily$fourier.order
## [1] 4
## 
## $seasonalities$daily$prior.scale
## [1] 10
## 
## $seasonalities$daily$mode
## [1] "additive"
## 
## $seasonalities$daily$condition.name
## NULL
## 
## 
## 
## $extra_regressors
## list()
## 
## $country_holidays
## NULL
## 
## $stan.fit
## $stan.fit$par
## $stan.fit$par$k
## [1] -0.3399185
## 
## $stan.fit$par$m
## [1] 0.3551693
## 
## $stan.fit$par$delta
##  [1]  7.557253e-08  3.483415e-08  2.688660e-01  4.799589e-01  2.004927e-01
##  [6]  6.476051e-08  5.903609e-08 -2.108516e-01 -2.755958e-01 -1.215397e-07
## [11]  4.155000e-08  2.488461e-07 -1.266203e-08 -3.357057e-03 -3.749413e-02
## [16] -1.522682e-08 -6.884554e-08  7.239539e-03  2.767627e-02  3.916694e-02
## [21]  7.126680e-02  1.687457e-02  3.888608e-03  1.302859e-07 -6.894206e-02
## 
## $stan.fit$par$sigma_obs
## [1] 0.02704036
## 
## $stan.fit$par$beta
##  [1] -1.503878e-02 -1.395354e-01 -2.416547e-02 -7.901517e-03 -1.777479e-02
##  [6] -2.432104e-02  7.693029e-03 -8.147217e-03  6.676297e-03 -1.188980e-02
## [11]  1.535229e-02  3.032079e-03  3.252465e-03  9.647003e-03  4.167203e-03
## [16]  5.074982e-03 -7.422047e-03  5.948540e-03 -4.875237e-03 -4.564492e-04
## [21]  7.696883e-02 -2.570810e-03 -4.462161e-02 -9.995736e-03  4.729456e-02
## [26]  6.687925e-03 -5.405959e-11  3.823590e-02 -1.081192e-10  3.823590e-02
## [31] -2.690668e-11  3.823590e-02 -2.162384e-10  3.823590e-02
## 
## $stan.fit$par$trend
##    [1] 0.3551693 0.3549365 0.3547037 0.3544709 0.3542380 0.3540052 0.3537724
##    [8] 0.3535396 0.3533068 0.3530739 0.3528411 0.3526083 0.3523755 0.3521427
##   [15] 0.3519098 0.3516770 0.3514442 0.3512114 0.3509785 0.3507457 0.3505129
##   [22] 0.3502801 0.3500473 0.3498144 0.3495816 0.3493488 0.3491160 0.3488832
##   [29] 0.3486503 0.3484175 0.3481847 0.3479519 0.3477191 0.3474862 0.3472534
##   [36] 0.3470206 0.3467878 0.3465550 0.3463221 0.3460893 0.3458565 0.3456237
##   [43] 0.3453908 0.3451580 0.3449252 0.3446924 0.3444596 0.3442267 0.3439939
##   [50] 0.3437611 0.3435283 0.3432955 0.3430626 0.3428298 0.3425970 0.3423642
##   [57] 0.3421314 0.3418985 0.3416657 0.3414329 0.3412001 0.3409673 0.3407344
##   [64] 0.3405016 0.3402688 0.3400360 0.3398031 0.3395703 0.3393375 0.3391047
##   [71] 0.3388719 0.3386390 0.3384062 0.3381734 0.3379406 0.3377078 0.3374749
##   [78] 0.3372421 0.3370093 0.3367765 0.3365437 0.3363108 0.3360780 0.3358452
##   [85] 0.3356124 0.3353796 0.3351467 0.3349139 0.3346811 0.3344483 0.3342154
##   [92] 0.3339826 0.3337498 0.3335170 0.3332842 0.3330513 0.3328185 0.3325857
##   [99] 0.3323529 0.3321201 0.3318872 0.3316544 0.3314216 0.3311888 0.3309560
##  [106] 0.3307231 0.3304903 0.3302575 0.3300247 0.3297919 0.3295590 0.3293262
##  [113] 0.3290934 0.3288606 0.3286277 0.3283949 0.3281621 0.3279293 0.3276965
##  [120] 0.3274636 0.3272308 0.3269980 0.3267652 0.3265324 0.3262995 0.3260667
##  [127] 0.3258339 0.3256011 0.3253683 0.3251354 0.3249026 0.3246698 0.3244370
##  [134] 0.3242042 0.3239713 0.3237385 0.3235057 0.3232729 0.3230400 0.3228072
##  [141] 0.3225744 0.3225257 0.3224771 0.3224284 0.3223797 0.3223311 0.3222824
##  [148] 0.3222337 0.3221851 0.3221364 0.3220877 0.3220391 0.3219904 0.3219417
##  [155] 0.3218931 0.3218444 0.3217957 0.3217471 0.3216984 0.3216498 0.3216011
##  [162] 0.3215524 0.3215038 0.3214551 0.3214064 0.3213578 0.3213091 0.3212604
##  [169] 0.3212118 0.3211631 0.3211144 0.3210658 0.3210171 0.3209684 0.3209198
##  [176] 0.3208711 0.3208224 0.3207738 0.3207251 0.3206764 0.3206278 0.3205791
##  [183] 0.3205304 0.3204818 0.3204331 0.3203844 0.3203358 0.3202871 0.3205672
##  [190] 0.3208472 0.3211273 0.3214074 0.3216875 0.3219675 0.3222476 0.3225277
##  [197] 0.3228078 0.3230878 0.3233679 0.3236480 0.3239280 0.3242081 0.3244882
##  [204] 0.3247683 0.3250483 0.3253284 0.3256085 0.3258886 0.3261686 0.3264487
##  [211] 0.3267288 0.3270089 0.3272889 0.3275690 0.3278491 0.3281291 0.3284092
##  [218] 0.3286893 0.3289694 0.3292494 0.3295295 0.3298096 0.3300897 0.3303697
##  [225] 0.3306498 0.3309299 0.3312099 0.3314900 0.3317701 0.3320502 0.3323302
##  [232] 0.3326103 0.3328904 0.3331705 0.3335879 0.3340052 0.3344226 0.3348400
##  [239] 0.3352574 0.3356748 0.3360922 0.3365096 0.3369270 0.3373444 0.3377618
##  [246] 0.3381792 0.3385966 0.3390140 0.3394314 0.3398488 0.3402662 0.3406836
##  [253] 0.3411010 0.3415184 0.3419358 0.3423532 0.3427706 0.3431880 0.3436054
##  [260] 0.3440228 0.3444402 0.3448576 0.3452750 0.3456924 0.3461098 0.3465272
##  [267] 0.3469445 0.3473619 0.3477793 0.3481967 0.3486141 0.3490315 0.3494489
##  [274] 0.3498663 0.3502837 0.3507011 0.3511185 0.3515359 0.3519533 0.3523707
##  [281] 0.3527881 0.3532055 0.3536229 0.3540403 0.3544577 0.3548751 0.3552925
##  [288] 0.3557099 0.3561273 0.3565447 0.3569621 0.3573795 0.3577969 0.3582143
##  [295] 0.3586317 0.3590491 0.3594665 0.3598838 0.3603012 0.3607186 0.3611360
##  [302] 0.3615534 0.3619708 0.3623882 0.3628056 0.3632230 0.3636404 0.3640578
##  [309] 0.3644752 0.3648926 0.3653100 0.3657274 0.3661448 0.3665622 0.3669796
##  [316] 0.3673970 0.3678144 0.3682318 0.3686492 0.3690666 0.3694840 0.3699014
##  [323] 0.3703188 0.3707362 0.3711536 0.3715710 0.3719884 0.3724057 0.3728231
##  [330] 0.3732405 0.3736579 0.3740753 0.3744927 0.3749101 0.3753275 0.3757449
##  [337] 0.3761623 0.3765797 0.3769971 0.3774145 0.3778319 0.3782493 0.3786667
##  [344] 0.3790841 0.3795015 0.3799189 0.3803363 0.3807537 0.3811711 0.3815885
##  [351] 0.3820059 0.3824233 0.3828407 0.3832581 0.3836755 0.3840929 0.3845103
##  [358] 0.3849277 0.3853451 0.3857624 0.3861798 0.3865972 0.3870146 0.3874320
##  [365] 0.3878494 0.3882668 0.3886842 0.3891016 0.3895190 0.3899364 0.3903538
##  [372] 0.3907712 0.3911886 0.3916060 0.3918790 0.3921520 0.3924249 0.3926979
##  [379] 0.3929709 0.3932439 0.3935168 0.3937898 0.3940628 0.3943358 0.3946088
##  [386] 0.3948817 0.3951547 0.3954277 0.3957007 0.3959736 0.3962466 0.3965196
##  [393] 0.3967926 0.3970656 0.3973385 0.3976115 0.3978845 0.3981575 0.3984305
##  [400] 0.3987034 0.3989764 0.3992494 0.3995224 0.3997953 0.4000683 0.4003413
##  [407] 0.4006143 0.4008873 0.4011602 0.4014332 0.4017062 0.4019792 0.4022521
##  [414] 0.4025251 0.4027981 0.4030711 0.4033441 0.4036170 0.4038900 0.4041630
##  [421] 0.4044360 0.4045202 0.4046044 0.4046886 0.4047728 0.4048570 0.4049412
##  [428] 0.4050255 0.4051097 0.4051939 0.4052781 0.4053623 0.4054465 0.4055307
##  [435] 0.4056150 0.4056992 0.4057834 0.4058676 0.4059518 0.4060360 0.4061202
##  [442] 0.4062045 0.4062887 0.4063729 0.4064571 0.4065413 0.4066255 0.4067097
##  [449] 0.4067939 0.4068782 0.4069624 0.4070466 0.4071308 0.4072150 0.4072992
##  [456] 0.4073834 0.4074677 0.4075519 0.4076361 0.4077203 0.4078045 0.4078887
##  [463] 0.4079729 0.4080572 0.4081414 0.4082256 0.4083098 0.4083940 0.4084782
##  [470] 0.4085624 0.4086466 0.4087309 0.4088151 0.4088993 0.4089835 0.4090677
##  [477] 0.4091519 0.4092361 0.4093204 0.4094046 0.4094888 0.4095730 0.4096572
##  [484] 0.4097414 0.4098256 0.4099099 0.4099941 0.4100783 0.4101625 0.4102467
##  [491] 0.4103309 0.4104151 0.4104993 0.4105836 0.4106678 0.4107520 0.4108362
##  [498] 0.4109204 0.4110046 0.4110888 0.4111731 0.4112573 0.4113415 0.4114257
##  [505] 0.4115099 0.4115941 0.4116783 0.4117626 0.4118468 0.4119310 0.4120152
##  [512] 0.4120994 0.4121836 0.4122678 0.4123520 0.4124363 0.4125205 0.4126047
##  [519] 0.4126889 0.4127731 0.4128573 0.4129415 0.4130258 0.4131100 0.4131942
##  [526] 0.4132784 0.4133626 0.4134468 0.4135310 0.4136153 0.4136995 0.4137837
##  [533] 0.4138679 0.4139521 0.4140363 0.4141205 0.4142047 0.4142890 0.4143732
##  [540] 0.4144574 0.4145416 0.4146258 0.4147100 0.4147942 0.4148785 0.4149627
##  [547] 0.4150469 0.4151311 0.4152153 0.4152995 0.4153837 0.4154679 0.4155522
##  [554] 0.4156364 0.4157206 0.4158048 0.4158890 0.4159732 0.4160574 0.4161417
##  [561] 0.4162259 0.4163101 0.4163943 0.4164785 0.4165627 0.4166469 0.4167312
##  [568] 0.4168154 0.4168996 0.4169838 0.4170680 0.4171522 0.4172364 0.4173207
##  [575] 0.4174049 0.4174891 0.4175733 0.4176575 0.4177417 0.4178259 0.4179101
##  [582] 0.4179944 0.4180786 0.4181628 0.4182470 0.4183312 0.4184154 0.4184996
##  [589] 0.4185839 0.4186681 0.4187523 0.4188365 0.4189207 0.4190049 0.4190891
##  [596] 0.4191734 0.4192576 0.4193418 0.4194260 0.4195102 0.4195944 0.4196786
##  [603] 0.4197629 0.4198471 0.4199313 0.4200155 0.4200997 0.4201839 0.4202681
##  [610] 0.4203523 0.4204366 0.4205208 0.4206050 0.4206892 0.4207734 0.4208576
##  [617] 0.4209418 0.4210261 0.4211103 0.4211945 0.4212787 0.4213629 0.4214471
##  [624] 0.4215313 0.4216156 0.4216998 0.4217840 0.4218682 0.4219524 0.4220366
##  [631] 0.4221208 0.4222051 0.4222893 0.4223735 0.4224577 0.4225419 0.4226261
##  [638] 0.4227103 0.4227945 0.4228788 0.4229630 0.4230472 0.4231314 0.4232156
##  [645] 0.4232998 0.4233840 0.4234683 0.4235525 0.4236367 0.4237209 0.4238051
##  [652] 0.4238893 0.4239735 0.4240578 0.4241420 0.4242239 0.4243058 0.4243877
##  [659] 0.4244696 0.4245515 0.4246335 0.4247154 0.4247973 0.4248792 0.4249611
##  [666] 0.4250430 0.4251249 0.4252069 0.4252888 0.4253707 0.4254526 0.4255345
##  [673] 0.4256164 0.4256983 0.4257803 0.4258622 0.4259441 0.4260260 0.4261079
##  [680] 0.4261898 0.4262717 0.4263537 0.4264356 0.4265175 0.4265994 0.4266813
##  [687] 0.4267632 0.4268451 0.4269271 0.4270090 0.4270909 0.4271728 0.4272547
##  [694] 0.4273366 0.4274185 0.4275005 0.4275824 0.4276643 0.4277462 0.4278281
##  [701] 0.4279100 0.4279663 0.4280225 0.4280787 0.4281350 0.4281912 0.4282474
##  [708] 0.4283037 0.4283599 0.4284161 0.4284724 0.4285286 0.4285848 0.4286411
##  [715] 0.4286973 0.4287535 0.4288098 0.4288660 0.4289222 0.4289785 0.4290347
##  [722] 0.4290909 0.4291472 0.4292034 0.4292596 0.4293159 0.4293721 0.4294283
##  [729] 0.4294846 0.4295408 0.4295970 0.4296533 0.4297095 0.4297657 0.4298220
##  [736] 0.4298782 0.4299344 0.4299907 0.4300469 0.4301031 0.4301594 0.4302156
##  [743] 0.4302718 0.4303281 0.4303843 0.4304405 0.4304968 0.4305530 0.4306092
##  [750] 0.4306655 0.4307217 0.4307779 0.4308342 0.4308904 0.4309466 0.4310029
##  [757] 0.4310591 0.4311153 0.4311716 0.4312278 0.4312840 0.4313403 0.4313965
##  [764] 0.4314527 0.4315090 0.4315652 0.4316214 0.4316777 0.4317339 0.4317901
##  [771] 0.4318464 0.4319026 0.4319588 0.4320151 0.4320713 0.4321275 0.4321838
##  [778] 0.4322400 0.4322962 0.4323525 0.4324087 0.4324649 0.4325212 0.4325774
##  [785] 0.4326336 0.4326899 0.4327461 0.4328023 0.4328586 0.4329148 0.4329710
##  [792] 0.4330273 0.4330835 0.4331397 0.4331960 0.4332522 0.4333084 0.4333647
##  [799] 0.4334209 0.4334771 0.4335334 0.4335896 0.4336458 0.4337021 0.4337583
##  [806] 0.4338145 0.4338708 0.4339270 0.4339832 0.4340395 0.4340957 0.4341520
##  [813] 0.4342082 0.4342644 0.4343207 0.4343769 0.4344331 0.4344894 0.4345456
##  [820] 0.4346018 0.4346581 0.4347143 0.4347705 0.4348268 0.4348830 0.4349392
##  [827] 0.4349955 0.4350517 0.4351079 0.4351642 0.4352204 0.4352766 0.4353329
##  [834] 0.4353891 0.4354453 0.4355016 0.4355578 0.4356140 0.4356703 0.4357265
##  [841] 0.4357827 0.4358439 0.4359051 0.4359663 0.4360275 0.4360887 0.4361499
##  [848] 0.4362111 0.4362723 0.4363334 0.4363946 0.4364558 0.4365170 0.4365782
##  [855] 0.4366394 0.4367006 0.4367618 0.4368230 0.4368842 0.4369454 0.4370066
##  [862] 0.4370678 0.4371289 0.4371901 0.4372513 0.4373125 0.4373737 0.4374349
##  [869] 0.4374961 0.4375573 0.4376185 0.4376797 0.4377409 0.4378021 0.4378632
##  [876] 0.4379244 0.4379856 0.4380468 0.4381080 0.4381692 0.4382304 0.4382916
##  [883] 0.4383528 0.4384140 0.4384752 0.4385364 0.4385976 0.4386587 0.4387389
##  [890] 0.4388190 0.4388992 0.4389793 0.4390595 0.4391396 0.4392198 0.4392999
##  [897] 0.4393801 0.4394602 0.4395404 0.4396205 0.4397007 0.4397808 0.4398610
##  [904] 0.4399411 0.4400213 0.4401014 0.4401816 0.4402617 0.4403419 0.4404220
##  [911] 0.4405022 0.4405823 0.4406625 0.4407426 0.4408228 0.4409029 0.4409830
##  [918] 0.4410632 0.4411433 0.4412235 0.4413036 0.4413838 0.4414639 0.4415441
##  [925] 0.4416242 0.4417044 0.4417845 0.4418647 0.4419448 0.4420250 0.4421051
##  [932] 0.4421853 0.4422654 0.4423456 0.4424257 0.4425327 0.4426397 0.4427466
##  [939] 0.4428536 0.4429606 0.4430676 0.4431745 0.4432815 0.4433885 0.4434955
##  [946] 0.4436024 0.4437094 0.4438164 0.4439234 0.4440303 0.4441373 0.4442443
##  [953] 0.4443513 0.4444582 0.4445652 0.4446722 0.4447792 0.4448861 0.4449931
##  [960] 0.4451001 0.4452071 0.4453140 0.4454210 0.4455280 0.4456350 0.4457419
##  [967] 0.4458489 0.4459559 0.4460629 0.4461698 0.4462768 0.4463838 0.4464908
##  [974] 0.4465977 0.4467047 0.4468117 0.4469187 0.4470256 0.4471326 0.4472396
##  [981] 0.4473466 0.4475024 0.4476581 0.4478139 0.4479697 0.4481255 0.4482813
##  [988] 0.4484371 0.4485929 0.4487487 0.4489045 0.4490602 0.4492160 0.4493718
##  [995] 0.4495276 0.4496834 0.4498392 0.4499950 0.4501508 0.4503065 0.4504623
## [1002] 0.4506181 0.4507739 0.4509297 0.4510855 0.4512413 0.4513971 0.4515528
## [1009] 0.4517086 0.4518644 0.4520202 0.4521760 0.4523318 0.4524876 0.4526434
## [1016] 0.4527992 0.4529549 0.4531107 0.4532665 0.4534223 0.4535781 0.4537339
## [1023] 0.4538897 0.4540455 0.4542012 0.4543570 0.4545128 0.4546686 0.4548360
## [1030] 0.4550033 0.4551706 0.4553380 0.4555053 0.4556727 0.4558400 0.4560074
## [1037] 0.4561747 0.4563421 0.4565094 0.4566768 0.4568441 0.4570114 0.4571788
## [1044] 0.4573461 0.4575135 0.4576808 0.4578482 0.4580155 0.4581829 0.4583502
## [1051] 0.4585176 0.4586849 0.4588523 0.4590196 0.4591869 0.4593543 0.4595216
## [1058] 0.4596890 0.4598563 0.4600237 0.4601910 0.4603584 0.4605257 0.4606931
## [1065] 0.4608604 0.4610277 0.4611951 0.4613624 0.4615298 0.4616971 0.4618645
## [1072] 0.4620318 0.4621992 0.4623665 0.4625339 0.4627039 0.4628739 0.4630439
## [1079] 0.4632139 0.4633839 0.4635539 0.4637239 0.4638939 0.4640639 0.4642340
## [1086] 0.4644040 0.4645740 0.4647440 0.4649140 0.4650840 0.4652540 0.4654240
## [1093] 0.4655940 0.4657640 0.4659340 0.4661041 0.4662741 0.4664441 0.4666141
## [1100] 0.4667841 0.4669541 0.4671241 0.4672941 0.4674641 0.4676341 0.4678042
## [1107] 0.4679742 0.4681442 0.4683142 0.4684842 0.4686542 0.4688242 0.4689942
## [1114] 0.4691642 0.4693342 0.4695042 0.4696743 0.4698443 0.4700143 0.4701843
## [1121] 0.4703543 0.4705243 0.4706943 0.4708643 0.4710343 0.4712043 0.4713743
## [1128] 0.4715444 0.4717144 0.4718844 0.4720544 0.4722244 0.4723944 0.4725644
## [1135] 0.4727344 0.4729044 0.4730744 0.4732444 0.4734145 0.4735845 0.4737545
## [1142] 0.4739245 0.4740945 0.4742645 0.4744345 0.4746045 0.4747745 0.4749445
## [1149] 0.4751146 0.4752846 0.4754546 0.4756246 0.4757946 0.4759646 0.4761346
## [1156] 0.4763046 0.4764746 0.4766446 0.4768146 0.4769847 0.4771547 0.4773247
## [1163] 0.4774947 0.4776647 0.4778347 0.4780047 0.4781747 0.4783447 0.4784675
## [1170] 0.4785903 0.4787131 0.4788359 0.4789587 0.4790815 0.4792043 0.4793270
## [1177] 0.4794498 0.4795726 0.4796954 0.4798182 0.4799410 0.4800638 0.4801866
## [1184] 0.4803094 0.4804321 0.4805549 0.4806777 0.4808005 0.4809233 0.4810461
## [1191] 0.4811689 0.4812917 0.4814145 0.4815372 0.4816600 0.4817828 0.4819056
## [1198] 0.4820284 0.4821512 0.4822740 0.4823968 0.4825195 0.4826423 0.4827651
## [1205] 0.4828879 0.4830107 0.4831335 0.4832563 0.4833791 0.4835019 0.4836246
## [1212] 0.4837474 0.4838702 0.4839930 0.4841158 0.4842386 0.4843614 0.4844842
## [1219] 0.4846070 0.4847297 0.4848525 0.4849753 0.4850981 0.4852209 0.4853437
## [1226] 0.4854665 0.4855893 0.4857121 0.4858348 0.4859576 0.4860804 0.4862032
## [1233] 0.4863260 0.4864488 0.4865716 0.4866944 0.4868172 0.4869399 0.4870627
## [1240] 0.4871855 0.4873083 0.4874311 0.4875539 0.4876767 0.4877995 0.4879223
## [1247] 0.4880450 0.4881678 0.4882906 0.4884134 0.4885362 0.4886590 0.4887818
## [1254] 0.4889046 0.4890274 0.4891501 0.4892729 0.4893957 0.4895185 0.4896413
## [1261] 0.4897641 0.4898869 0.4900097 0.4901325 0.4902552 0.4903780 0.4905008
## [1268] 0.4906236 0.4907464 0.4908692 0.4909920 0.4911148 0.4912376 0.4913603
## [1275] 0.4914831 0.4916059 0.4917287 0.4918515 0.4919743 0.4920971 0.4922199
## [1282] 0.4923427 0.4924654 0.4925882 0.4927110 0.4928338 0.4929566 0.4930794
## [1289] 0.4932022 0.4933250 0.4934478 0.4935705 0.4936933 0.4938161 0.4939389
## [1296] 0.4940617 0.4941845 0.4943073 0.4944301 0.4945529 0.4946756 0.4947984
## [1303] 0.4949212 0.4950440 0.4951668 0.4952896 0.4954124 0.4955352 0.4956580
## [1310] 0.4957807 0.4959035 0.4960263 0.4961491 0.4962719 0.4963947 0.4965175
## [1317] 0.4966403 0.4967630 0.4968858 0.4970086 0.4971314 0.4972542 0.4973770
## [1324] 0.4974998 0.4976226 0.4977454 0.4978681 0.4979909 0.4981137 0.4982365
## [1331] 0.4983593 0.4984821 0.4986049 0.4987277 0.4988505 0.4989732 0.4990960
## [1338] 0.4992188 0.4993416 0.4994644 0.4995872 0.4997100 0.4998328 0.4999556
## [1345] 0.5000783 0.5002011 0.5003239 0.5004467 0.5005695 0.5006923 0.5008151
## [1352] 0.5009379 0.5010607 0.5011834 0.5013062 0.5014290 0.5015518 0.5016746
## [1359] 0.5017974 0.5019202 0.5020430 0.5021658 0.5022885 0.5024113 0.5025341
## [1366] 0.5026569 0.5027797 0.5029025 0.5030253 0.5031481 0.5032709 0.5033936
## [1373] 0.5035164 0.5036392 0.5037620 0.5038848 0.5040076 0.5041304 0.5042532
## [1380] 0.5043760 0.5044987 0.5046215 0.5047443 0.5048671 0.5049899 0.5051127
## [1387] 0.5052355 0.5053583 0.5054811 0.5056038 0.5057266 0.5058494 0.5059722
## [1394] 0.5060950 0.5062178 0.5063406 0.5064634 0.5065862 0.5067089 0.5068317
## [1401] 0.5069545 0.5070773 0.5072001 0.5073229 0.5074457 0.5075685 0.5076913
## [1408] 0.5078140 0.5079368 0.5080596 0.5081824 0.5083052 0.5084280 0.5085508
## [1415] 0.5086736 0.5087964 0.5089191 0.5090419 0.5091647 0.5092875 0.5094103
## [1422] 0.5095331 0.5096559 0.5097787 0.5099015 0.5100242 0.5101470 0.5102698
## [1429] 0.5103926 0.5105154 0.5106382 0.5107610 0.5108838 0.5110065 0.5111293
## [1436] 0.5112521 0.5113749 0.5114977 0.5116205 0.5117433 0.5118661 0.5119889
## [1443] 0.5121116 0.5122344 0.5123572 0.5124800 0.5126028 0.5127256 0.5128484
## [1450] 0.5129712 0.5130940 0.5132167 0.5133395 0.5134623 0.5135851 0.5137079
## [1457] 0.5138307 0.5139535 0.5140763 0.5141991 0.5143218
## 
## 
## $stan.fit$value
## [1] 4510.037
## 
## $stan.fit$return_code
## [1] 0
## 
## $stan.fit$theta_tilde
##               k         m     delta[1]     delta[2] delta[3]  delta[4]
## [1,] -0.3399185 0.3551693 7.557253e-08 3.483415e-08 0.268866 0.4799589
##       delta[5]     delta[6]     delta[7]   delta[8]   delta[9]     delta[10]
## [1,] 0.2004927 6.476051e-08 5.903609e-08 -0.2108516 -0.2755958 -1.215397e-07
##      delta[11]    delta[12]     delta[13]    delta[14]   delta[15]
## [1,] 4.155e-08 2.488461e-07 -1.266203e-08 -0.003357057 -0.03749413
##          delta[16]     delta[17]   delta[18]  delta[19]  delta[20] delta[21]
## [1,] -1.522682e-08 -6.884554e-08 0.007239539 0.02767627 0.03916694 0.0712668
##       delta[22]   delta[23]    delta[24]   delta[25]  sigma_obs     beta[1]
## [1,] 0.01687457 0.003888608 1.302859e-07 -0.06894206 0.02704036 -0.01503878
##         beta[2]     beta[3]      beta[4]     beta[5]     beta[6]     beta[7]
## [1,] -0.1395354 -0.02416547 -0.007901517 -0.01777479 -0.02432104 0.007693029
##           beta[8]     beta[9]   beta[10]   beta[11]    beta[12]    beta[13]
## [1,] -0.008147217 0.006676297 -0.0118898 0.01535229 0.003032079 0.003252465
##         beta[14]    beta[15]    beta[16]     beta[17]   beta[18]     beta[19]
## [1,] 0.009647003 0.004167203 0.005074982 -0.007422047 0.00594854 -0.004875237
##           beta[20]   beta[21]    beta[22]    beta[23]     beta[24]   beta[25]
## [1,] -0.0004564492 0.07696883 -0.00257081 -0.04462161 -0.009995736 0.04729456
##         beta[26]      beta[27]  beta[28]      beta[29]  beta[30]      beta[31]
## [1,] 0.006687925 -5.405959e-11 0.0382359 -1.081192e-10 0.0382359 -2.690668e-11
##       beta[32]      beta[33]  beta[34]  trend[1]  trend[2]  trend[3]  trend[4]
## [1,] 0.0382359 -2.162384e-10 0.0382359 0.3551693 0.3549365 0.3547037 0.3544709
##      trend[5]  trend[6]  trend[7]  trend[8]  trend[9] trend[10] trend[11]
## [1,] 0.354238 0.3540052 0.3537724 0.3535396 0.3533068 0.3530739 0.3528411
##      trend[12] trend[13] trend[14] trend[15] trend[16] trend[17] trend[18]
## [1,] 0.3526083 0.3523755 0.3521427 0.3519098  0.351677 0.3514442 0.3512114
##      trend[19] trend[20] trend[21] trend[22] trend[23] trend[24] trend[25]
## [1,] 0.3509785 0.3507457 0.3505129 0.3502801 0.3500473 0.3498144 0.3495816
##      trend[26] trend[27] trend[28] trend[29] trend[30] trend[31] trend[32]
## [1,] 0.3493488  0.349116 0.3488832 0.3486503 0.3484175 0.3481847 0.3479519
##      trend[33] trend[34] trend[35] trend[36] trend[37] trend[38] trend[39]
## [1,] 0.3477191 0.3474862 0.3472534 0.3470206 0.3467878  0.346555 0.3463221
##      trend[40] trend[41] trend[42] trend[43] trend[44] trend[45] trend[46]
## [1,] 0.3460893 0.3458565 0.3456237 0.3453908  0.345158 0.3449252 0.3446924
##      trend[47] trend[48] trend[49] trend[50] trend[51] trend[52] trend[53]
## [1,] 0.3444596 0.3442267 0.3439939 0.3437611 0.3435283 0.3432955 0.3430626
##      trend[54] trend[55] trend[56] trend[57] trend[58] trend[59] trend[60]
## [1,] 0.3428298  0.342597 0.3423642 0.3421314 0.3418985 0.3416657 0.3414329
##      trend[61] trend[62] trend[63] trend[64] trend[65] trend[66] trend[67]
## [1,] 0.3412001 0.3409673 0.3407344 0.3405016 0.3402688  0.340036 0.3398031
##      trend[68] trend[69] trend[70] trend[71] trend[72] trend[73] trend[74]
## [1,] 0.3395703 0.3393375 0.3391047 0.3388719  0.338639 0.3384062 0.3381734
##      trend[75] trend[76] trend[77] trend[78] trend[79] trend[80] trend[81]
## [1,] 0.3379406 0.3377078 0.3374749 0.3372421 0.3370093 0.3367765 0.3365437
##      trend[82] trend[83] trend[84] trend[85] trend[86] trend[87] trend[88]
## [1,] 0.3363108  0.336078 0.3358452 0.3356124 0.3353796 0.3351467 0.3349139
##      trend[89] trend[90] trend[91] trend[92] trend[93] trend[94] trend[95]
## [1,] 0.3346811 0.3344483 0.3342154 0.3339826 0.3337498  0.333517 0.3332842
##      trend[96] trend[97] trend[98] trend[99] trend[100] trend[101] trend[102]
## [1,] 0.3330513 0.3328185 0.3325857 0.3323529  0.3321201  0.3318872  0.3316544
##      trend[103] trend[104] trend[105] trend[106] trend[107] trend[108]
## [1,]  0.3314216  0.3311888   0.330956  0.3307231  0.3304903  0.3302575
##      trend[109] trend[110] trend[111] trend[112] trend[113] trend[114]
## [1,]  0.3300247  0.3297919   0.329559  0.3293262  0.3290934  0.3288606
##      trend[115] trend[116] trend[117] trend[118] trend[119] trend[120]
## [1,]  0.3286277  0.3283949  0.3281621  0.3279293  0.3276965  0.3274636
##      trend[121] trend[122] trend[123] trend[124] trend[125] trend[126]
## [1,]  0.3272308   0.326998  0.3267652  0.3265324  0.3262995  0.3260667
##      trend[127] trend[128] trend[129] trend[130] trend[131] trend[132]
## [1,]  0.3258339  0.3256011  0.3253683  0.3251354  0.3249026  0.3246698
##      trend[133] trend[134] trend[135] trend[136] trend[137] trend[138]
## [1,]   0.324437  0.3242042  0.3239713  0.3237385  0.3235057  0.3232729
##      trend[139] trend[140] trend[141] trend[142] trend[143] trend[144]
## [1,]    0.32304  0.3228072  0.3225744  0.3225257  0.3224771  0.3224284
##      trend[145] trend[146] trend[147] trend[148] trend[149] trend[150]
## [1,]  0.3223797  0.3223311  0.3222824  0.3222337  0.3221851  0.3221364
##      trend[151] trend[152] trend[153] trend[154] trend[155] trend[156]
## [1,]  0.3220877  0.3220391  0.3219904  0.3219417  0.3218931  0.3218444
##      trend[157] trend[158] trend[159] trend[160] trend[161] trend[162]
## [1,]  0.3217957  0.3217471  0.3216984  0.3216498  0.3216011  0.3215524
##      trend[163] trend[164] trend[165] trend[166] trend[167] trend[168]
## [1,]  0.3215038  0.3214551  0.3214064  0.3213578  0.3213091  0.3212604
##      trend[169] trend[170] trend[171] trend[172] trend[173] trend[174]
## [1,]  0.3212118  0.3211631  0.3211144  0.3210658  0.3210171  0.3209684
##      trend[175] trend[176] trend[177] trend[178] trend[179] trend[180]
## [1,]  0.3209198  0.3208711  0.3208224  0.3207738  0.3207251  0.3206764
##      trend[181] trend[182] trend[183] trend[184] trend[185] trend[186]
## [1,]  0.3206278  0.3205791  0.3205304  0.3204818  0.3204331  0.3203844
##      trend[187] trend[188] trend[189] trend[190] trend[191] trend[192]
## [1,]  0.3203358  0.3202871  0.3205672  0.3208472  0.3211273  0.3214074
##      trend[193] trend[194] trend[195] trend[196] trend[197] trend[198]
## [1,]  0.3216875  0.3219675  0.3222476  0.3225277  0.3228078  0.3230878
##      trend[199] trend[200] trend[201] trend[202] trend[203] trend[204]
## [1,]  0.3233679   0.323648   0.323928  0.3242081  0.3244882  0.3247683
##      trend[205] trend[206] trend[207] trend[208] trend[209] trend[210]
## [1,]  0.3250483  0.3253284  0.3256085  0.3258886  0.3261686  0.3264487
##      trend[211] trend[212] trend[213] trend[214] trend[215] trend[216]
## [1,]  0.3267288  0.3270089  0.3272889   0.327569  0.3278491  0.3281291
##      trend[217] trend[218] trend[219] trend[220] trend[221] trend[222]
## [1,]  0.3284092  0.3286893  0.3289694  0.3292494  0.3295295  0.3298096
##      trend[223] trend[224] trend[225] trend[226] trend[227] trend[228]
## [1,]  0.3300897  0.3303697  0.3306498  0.3309299  0.3312099    0.33149
##      trend[229] trend[230] trend[231] trend[232] trend[233] trend[234]
## [1,]  0.3317701  0.3320502  0.3323302  0.3326103  0.3328904  0.3331705
##      trend[235] trend[236] trend[237] trend[238] trend[239] trend[240]
## [1,]  0.3335879  0.3340052  0.3344226    0.33484  0.3352574  0.3356748
##      trend[241] trend[242] trend[243] trend[244] trend[245] trend[246]
## [1,]  0.3360922  0.3365096   0.336927  0.3373444  0.3377618  0.3381792
##      trend[247] trend[248] trend[249] trend[250] trend[251] trend[252]
## [1,]  0.3385966   0.339014  0.3394314  0.3398488  0.3402662  0.3406836
##      trend[253] trend[254] trend[255] trend[256] trend[257] trend[258]
## [1,]   0.341101  0.3415184  0.3419358  0.3423532  0.3427706   0.343188
##      trend[259] trend[260] trend[261] trend[262] trend[263] trend[264]
## [1,]  0.3436054  0.3440228  0.3444402  0.3448576   0.345275  0.3456924
##      trend[265] trend[266] trend[267] trend[268] trend[269] trend[270]
## [1,]  0.3461098  0.3465272  0.3469445  0.3473619  0.3477793  0.3481967
##      trend[271] trend[272] trend[273] trend[274] trend[275] trend[276]
## [1,]  0.3486141  0.3490315  0.3494489  0.3498663  0.3502837  0.3507011
##      trend[277] trend[278] trend[279] trend[280] trend[281] trend[282]
## [1,]  0.3511185  0.3515359  0.3519533  0.3523707  0.3527881  0.3532055
##      trend[283] trend[284] trend[285] trend[286] trend[287] trend[288]
## [1,]  0.3536229  0.3540403  0.3544577  0.3548751  0.3552925  0.3557099
##      trend[289] trend[290] trend[291] trend[292] trend[293] trend[294]
## [1,]  0.3561273  0.3565447  0.3569621  0.3573795  0.3577969  0.3582143
##      trend[295] trend[296] trend[297] trend[298] trend[299] trend[300]
## [1,]  0.3586317  0.3590491  0.3594665  0.3598838  0.3603012  0.3607186
##      trend[301] trend[302] trend[303] trend[304] trend[305] trend[306]
## [1,]   0.361136  0.3615534  0.3619708  0.3623882  0.3628056   0.363223
##      trend[307] trend[308] trend[309] trend[310] trend[311] trend[312]
## [1,]  0.3636404  0.3640578  0.3644752  0.3648926    0.36531  0.3657274
##      trend[313] trend[314] trend[315] trend[316] trend[317] trend[318]
## [1,]  0.3661448  0.3665622  0.3669796   0.367397  0.3678144  0.3682318
##      trend[319] trend[320] trend[321] trend[322] trend[323] trend[324]
## [1,]  0.3686492  0.3690666   0.369484  0.3699014  0.3703188  0.3707362
##      trend[325] trend[326] trend[327] trend[328] trend[329] trend[330]
## [1,]  0.3711536   0.371571  0.3719884  0.3724057  0.3728231  0.3732405
##      trend[331] trend[332] trend[333] trend[334] trend[335] trend[336]
## [1,]  0.3736579  0.3740753  0.3744927  0.3749101  0.3753275  0.3757449
##      trend[337] trend[338] trend[339] trend[340] trend[341] trend[342]
## [1,]  0.3761623  0.3765797  0.3769971  0.3774145  0.3778319  0.3782493
##      trend[343] trend[344] trend[345] trend[346] trend[347] trend[348]
## [1,]  0.3786667  0.3790841  0.3795015  0.3799189  0.3803363  0.3807537
##      trend[349] trend[350] trend[351] trend[352] trend[353] trend[354]
## [1,]  0.3811711  0.3815885  0.3820059  0.3824233  0.3828407  0.3832581
##      trend[355] trend[356] trend[357] trend[358] trend[359] trend[360]
## [1,]  0.3836755  0.3840929  0.3845103  0.3849277  0.3853451  0.3857624
##      trend[361] trend[362] trend[363] trend[364] trend[365] trend[366]
## [1,]  0.3861798  0.3865972  0.3870146   0.387432  0.3878494  0.3882668
##      trend[367] trend[368] trend[369] trend[370] trend[371] trend[372]
## [1,]  0.3886842  0.3891016   0.389519  0.3899364  0.3903538  0.3907712
##      trend[373] trend[374] trend[375] trend[376] trend[377] trend[378]
## [1,]  0.3911886   0.391606   0.391879   0.392152  0.3924249  0.3926979
##      trend[379] trend[380] trend[381] trend[382] trend[383] trend[384]
## [1,]  0.3929709  0.3932439  0.3935168  0.3937898  0.3940628  0.3943358
##      trend[385] trend[386] trend[387] trend[388] trend[389] trend[390]
## [1,]  0.3946088  0.3948817  0.3951547  0.3954277  0.3957007  0.3959736
##      trend[391] trend[392] trend[393] trend[394] trend[395] trend[396]
## [1,]  0.3962466  0.3965196  0.3967926  0.3970656  0.3973385  0.3976115
##      trend[397] trend[398] trend[399] trend[400] trend[401] trend[402]
## [1,]  0.3978845  0.3981575  0.3984305  0.3987034  0.3989764  0.3992494
##      trend[403] trend[404] trend[405] trend[406] trend[407] trend[408]
## [1,]  0.3995224  0.3997953  0.4000683  0.4003413  0.4006143  0.4008873
##      trend[409] trend[410] trend[411] trend[412] trend[413] trend[414]
## [1,]  0.4011602  0.4014332  0.4017062  0.4019792  0.4022521  0.4025251
##      trend[415] trend[416] trend[417] trend[418] trend[419] trend[420]
## [1,]  0.4027981  0.4030711  0.4033441   0.403617    0.40389   0.404163
##      trend[421] trend[422] trend[423] trend[424] trend[425] trend[426]
## [1,]   0.404436  0.4045202  0.4046044  0.4046886  0.4047728   0.404857
##      trend[427] trend[428] trend[429] trend[430] trend[431] trend[432]
## [1,]  0.4049412  0.4050255  0.4051097  0.4051939  0.4052781  0.4053623
##      trend[433] trend[434] trend[435] trend[436] trend[437] trend[438]
## [1,]  0.4054465  0.4055307   0.405615  0.4056992  0.4057834  0.4058676
##      trend[439] trend[440] trend[441] trend[442] trend[443] trend[444]
## [1,]  0.4059518   0.406036  0.4061202  0.4062045  0.4062887  0.4063729
##      trend[445] trend[446] trend[447] trend[448] trend[449] trend[450]
## [1,]  0.4064571  0.4065413  0.4066255  0.4067097  0.4067939  0.4068782
##      trend[451] trend[452] trend[453] trend[454] trend[455] trend[456]
## [1,]  0.4069624  0.4070466  0.4071308   0.407215  0.4072992  0.4073834
##      trend[457] trend[458] trend[459] trend[460] trend[461] trend[462]
## [1,]  0.4074677  0.4075519  0.4076361  0.4077203  0.4078045  0.4078887
##      trend[463] trend[464] trend[465] trend[466] trend[467] trend[468]
## [1,]  0.4079729  0.4080572  0.4081414  0.4082256  0.4083098   0.408394
##      trend[469] trend[470] trend[471] trend[472] trend[473] trend[474]
## [1,]  0.4084782  0.4085624  0.4086466  0.4087309  0.4088151  0.4088993
##      trend[475] trend[476] trend[477] trend[478] trend[479] trend[480]
## [1,]  0.4089835  0.4090677  0.4091519  0.4092361  0.4093204  0.4094046
##      trend[481] trend[482] trend[483] trend[484] trend[485] trend[486]
## [1,]  0.4094888   0.409573  0.4096572  0.4097414  0.4098256  0.4099099
##      trend[487] trend[488] trend[489] trend[490] trend[491] trend[492]
## [1,]  0.4099941  0.4100783  0.4101625  0.4102467  0.4103309  0.4104151
##      trend[493] trend[494] trend[495] trend[496] trend[497] trend[498]
## [1,]  0.4104993  0.4105836  0.4106678   0.410752  0.4108362  0.4109204
##      trend[499] trend[500] trend[501] trend[502] trend[503] trend[504]
## [1,]  0.4110046  0.4110888  0.4111731  0.4112573  0.4113415  0.4114257
##      trend[505] trend[506] trend[507] trend[508] trend[509] trend[510]
## [1,]  0.4115099  0.4115941  0.4116783  0.4117626  0.4118468   0.411931
##      trend[511] trend[512] trend[513] trend[514] trend[515] trend[516]
## [1,]  0.4120152  0.4120994  0.4121836  0.4122678   0.412352  0.4124363
##      trend[517] trend[518] trend[519] trend[520] trend[521] trend[522]
## [1,]  0.4125205  0.4126047  0.4126889  0.4127731  0.4128573  0.4129415
##      trend[523] trend[524] trend[525] trend[526] trend[527] trend[528]
## [1,]  0.4130258    0.41311  0.4131942  0.4132784  0.4133626  0.4134468
##      trend[529] trend[530] trend[531] trend[532] trend[533] trend[534]
## [1,]   0.413531  0.4136153  0.4136995  0.4137837  0.4138679  0.4139521
##      trend[535] trend[536] trend[537] trend[538] trend[539] trend[540]
## [1,]  0.4140363  0.4141205  0.4142047   0.414289  0.4143732  0.4144574
##      trend[541] trend[542] trend[543] trend[544] trend[545] trend[546]
## [1,]  0.4145416  0.4146258    0.41471  0.4147942  0.4148785  0.4149627
##      trend[547] trend[548] trend[549] trend[550] trend[551] trend[552]
## [1,]  0.4150469  0.4151311  0.4152153  0.4152995  0.4153837  0.4154679
##      trend[553] trend[554] trend[555] trend[556] trend[557] trend[558]
## [1,]  0.4155522  0.4156364  0.4157206  0.4158048   0.415889  0.4159732
##      trend[559] trend[560] trend[561] trend[562] trend[563] trend[564]
## [1,]  0.4160574  0.4161417  0.4162259  0.4163101  0.4163943  0.4164785
##      trend[565] trend[566] trend[567] trend[568] trend[569] trend[570]
## [1,]  0.4165627  0.4166469  0.4167312  0.4168154  0.4168996  0.4169838
##      trend[571] trend[572] trend[573] trend[574] trend[575] trend[576]
## [1,]   0.417068  0.4171522  0.4172364  0.4173207  0.4174049  0.4174891
##      trend[577] trend[578] trend[579] trend[580] trend[581] trend[582]
## [1,]  0.4175733  0.4176575  0.4177417  0.4178259  0.4179101  0.4179944
##      trend[583] trend[584] trend[585] trend[586] trend[587] trend[588]
## [1,]  0.4180786  0.4181628   0.418247  0.4183312  0.4184154  0.4184996
##      trend[589] trend[590] trend[591] trend[592] trend[593] trend[594]
## [1,]  0.4185839  0.4186681  0.4187523  0.4188365  0.4189207  0.4190049
##      trend[595] trend[596] trend[597] trend[598] trend[599] trend[600]
## [1,]  0.4190891  0.4191734  0.4192576  0.4193418   0.419426  0.4195102
##      trend[601] trend[602] trend[603] trend[604] trend[605] trend[606]
## [1,]  0.4195944  0.4196786  0.4197629  0.4198471  0.4199313  0.4200155
##      trend[607] trend[608] trend[609] trend[610] trend[611] trend[612]
## [1,]  0.4200997  0.4201839  0.4202681  0.4203523  0.4204366  0.4205208
##      trend[613] trend[614] trend[615] trend[616] trend[617] trend[618]
## [1,]   0.420605  0.4206892  0.4207734  0.4208576  0.4209418  0.4210261
##      trend[619] trend[620] trend[621] trend[622] trend[623] trend[624]
## [1,]  0.4211103  0.4211945  0.4212787  0.4213629  0.4214471  0.4215313
##      trend[625] trend[626] trend[627] trend[628] trend[629] trend[630]
## [1,]  0.4216156  0.4216998   0.421784  0.4218682  0.4219524  0.4220366
##      trend[631] trend[632] trend[633] trend[634] trend[635] trend[636]
## [1,]  0.4221208  0.4222051  0.4222893  0.4223735  0.4224577  0.4225419
##      trend[637] trend[638] trend[639] trend[640] trend[641] trend[642]
## [1,]  0.4226261  0.4227103  0.4227945  0.4228788   0.422963  0.4230472
##      trend[643] trend[644] trend[645] trend[646] trend[647] trend[648]
## [1,]  0.4231314  0.4232156  0.4232998   0.423384  0.4234683  0.4235525
##      trend[649] trend[650] trend[651] trend[652] trend[653] trend[654]
## [1,]  0.4236367  0.4237209  0.4238051  0.4238893  0.4239735  0.4240578
##      trend[655] trend[656] trend[657] trend[658] trend[659] trend[660]
## [1,]   0.424142  0.4242239  0.4243058  0.4243877  0.4244696  0.4245515
##      trend[661] trend[662] trend[663] trend[664] trend[665] trend[666]
## [1,]  0.4246335  0.4247154  0.4247973  0.4248792  0.4249611   0.425043
##      trend[667] trend[668] trend[669] trend[670] trend[671] trend[672]
## [1,]  0.4251249  0.4252069  0.4252888  0.4253707  0.4254526  0.4255345
##      trend[673] trend[674] trend[675] trend[676] trend[677] trend[678]
## [1,]  0.4256164  0.4256983  0.4257803  0.4258622  0.4259441   0.426026
##      trend[679] trend[680] trend[681] trend[682] trend[683] trend[684]
## [1,]  0.4261079  0.4261898  0.4262717  0.4263537  0.4264356  0.4265175
##      trend[685] trend[686] trend[687] trend[688] trend[689] trend[690]
## [1,]  0.4265994  0.4266813  0.4267632  0.4268451  0.4269271   0.427009
##      trend[691] trend[692] trend[693] trend[694] trend[695] trend[696]
## [1,]  0.4270909  0.4271728  0.4272547  0.4273366  0.4274185  0.4275005
##      trend[697] trend[698] trend[699] trend[700] trend[701] trend[702]
## [1,]  0.4275824  0.4276643  0.4277462  0.4278281    0.42791  0.4279663
##      trend[703] trend[704] trend[705] trend[706] trend[707] trend[708]
## [1,]  0.4280225  0.4280787   0.428135  0.4281912  0.4282474  0.4283037
##      trend[709] trend[710] trend[711] trend[712] trend[713] trend[714]
## [1,]  0.4283599  0.4284161  0.4284724  0.4285286  0.4285848  0.4286411
##      trend[715] trend[716] trend[717] trend[718] trend[719] trend[720]
## [1,]  0.4286973  0.4287535  0.4288098   0.428866  0.4289222  0.4289785
##      trend[721] trend[722] trend[723] trend[724] trend[725] trend[726]
## [1,]  0.4290347  0.4290909  0.4291472  0.4292034  0.4292596  0.4293159
##      trend[727] trend[728] trend[729] trend[730] trend[731] trend[732]
## [1,]  0.4293721  0.4294283  0.4294846  0.4295408   0.429597  0.4296533
##      trend[733] trend[734] trend[735] trend[736] trend[737] trend[738]
## [1,]  0.4297095  0.4297657   0.429822  0.4298782  0.4299344  0.4299907
##      trend[739] trend[740] trend[741] trend[742] trend[743] trend[744]
## [1,]  0.4300469  0.4301031  0.4301594  0.4302156  0.4302718  0.4303281
##      trend[745] trend[746] trend[747] trend[748] trend[749] trend[750]
## [1,]  0.4303843  0.4304405  0.4304968   0.430553  0.4306092  0.4306655
##      trend[751] trend[752] trend[753] trend[754] trend[755] trend[756]
## [1,]  0.4307217  0.4307779  0.4308342  0.4308904  0.4309466  0.4310029
##      trend[757] trend[758] trend[759] trend[760] trend[761] trend[762]
## [1,]  0.4310591  0.4311153  0.4311716  0.4312278   0.431284  0.4313403
##      trend[763] trend[764] trend[765] trend[766] trend[767] trend[768]
## [1,]  0.4313965  0.4314527   0.431509  0.4315652  0.4316214  0.4316777
##      trend[769] trend[770] trend[771] trend[772] trend[773] trend[774]
## [1,]  0.4317339  0.4317901  0.4318464  0.4319026  0.4319588  0.4320151
##      trend[775] trend[776] trend[777] trend[778] trend[779] trend[780]
## [1,]  0.4320713  0.4321275  0.4321838    0.43224  0.4322962  0.4323525
##      trend[781] trend[782] trend[783] trend[784] trend[785] trend[786]
## [1,]  0.4324087  0.4324649  0.4325212  0.4325774  0.4326336  0.4326899
##      trend[787] trend[788] trend[789] trend[790] trend[791] trend[792]
## [1,]  0.4327461  0.4328023  0.4328586  0.4329148   0.432971  0.4330273
##      trend[793] trend[794] trend[795] trend[796] trend[797] trend[798]
## [1,]  0.4330835  0.4331397   0.433196  0.4332522  0.4333084  0.4333647
##      trend[799] trend[800] trend[801] trend[802] trend[803] trend[804]
## [1,]  0.4334209  0.4334771  0.4335334  0.4335896  0.4336458  0.4337021
##      trend[805] trend[806] trend[807] trend[808] trend[809] trend[810]
## [1,]  0.4337583  0.4338145  0.4338708   0.433927  0.4339832  0.4340395
##      trend[811] trend[812] trend[813] trend[814] trend[815] trend[816]
## [1,]  0.4340957   0.434152  0.4342082  0.4342644  0.4343207  0.4343769
##      trend[817] trend[818] trend[819] trend[820] trend[821] trend[822]
## [1,]  0.4344331  0.4344894  0.4345456  0.4346018  0.4346581  0.4347143
##      trend[823] trend[824] trend[825] trend[826] trend[827] trend[828]
## [1,]  0.4347705  0.4348268   0.434883  0.4349392  0.4349955  0.4350517
##      trend[829] trend[830] trend[831] trend[832] trend[833] trend[834]
## [1,]  0.4351079  0.4351642  0.4352204  0.4352766  0.4353329  0.4353891
##      trend[835] trend[836] trend[837] trend[838] trend[839] trend[840]
## [1,]  0.4354453  0.4355016  0.4355578   0.435614  0.4356703  0.4357265
##      trend[841] trend[842] trend[843] trend[844] trend[845] trend[846]
## [1,]  0.4357827  0.4358439  0.4359051  0.4359663  0.4360275  0.4360887
##      trend[847] trend[848] trend[849] trend[850] trend[851] trend[852]
## [1,]  0.4361499  0.4362111  0.4362723  0.4363334  0.4363946  0.4364558
##      trend[853] trend[854] trend[855] trend[856] trend[857] trend[858]
## [1,]   0.436517  0.4365782  0.4366394  0.4367006  0.4367618   0.436823
##      trend[859] trend[860] trend[861] trend[862] trend[863] trend[864]
## [1,]  0.4368842  0.4369454  0.4370066  0.4370678  0.4371289  0.4371901
##      trend[865] trend[866] trend[867] trend[868] trend[869] trend[870]
## [1,]  0.4372513  0.4373125  0.4373737  0.4374349  0.4374961  0.4375573
##      trend[871] trend[872] trend[873] trend[874] trend[875] trend[876]
## [1,]  0.4376185  0.4376797  0.4377409  0.4378021  0.4378632  0.4379244
##      trend[877] trend[878] trend[879] trend[880] trend[881] trend[882]
## [1,]  0.4379856  0.4380468   0.438108  0.4381692  0.4382304  0.4382916
##      trend[883] trend[884] trend[885] trend[886] trend[887] trend[888]
## [1,]  0.4383528   0.438414  0.4384752  0.4385364  0.4385976  0.4386587
##      trend[889] trend[890] trend[891] trend[892] trend[893] trend[894]
## [1,]  0.4387389   0.438819  0.4388992  0.4389793  0.4390595  0.4391396
##      trend[895] trend[896] trend[897] trend[898] trend[899] trend[900]
## [1,]  0.4392198  0.4392999  0.4393801  0.4394602  0.4395404  0.4396205
##      trend[901] trend[902] trend[903] trend[904] trend[905] trend[906]
## [1,]  0.4397007  0.4397808   0.439861  0.4399411  0.4400213  0.4401014
##      trend[907] trend[908] trend[909] trend[910] trend[911] trend[912]
## [1,]  0.4401816  0.4402617  0.4403419   0.440422  0.4405022  0.4405823
##      trend[913] trend[914] trend[915] trend[916] trend[917] trend[918]
## [1,]  0.4406625  0.4407426  0.4408228  0.4409029   0.440983  0.4410632
##      trend[919] trend[920] trend[921] trend[922] trend[923] trend[924]
## [1,]  0.4411433  0.4412235  0.4413036  0.4413838  0.4414639  0.4415441
##      trend[925] trend[926] trend[927] trend[928] trend[929] trend[930]
## [1,]  0.4416242  0.4417044  0.4417845  0.4418647  0.4419448   0.442025
##      trend[931] trend[932] trend[933] trend[934] trend[935] trend[936]
## [1,]  0.4421051  0.4421853  0.4422654  0.4423456  0.4424257  0.4425327
##      trend[937] trend[938] trend[939] trend[940] trend[941] trend[942]
## [1,]  0.4426397  0.4427466  0.4428536  0.4429606  0.4430676  0.4431745
##      trend[943] trend[944] trend[945] trend[946] trend[947] trend[948]
## [1,]  0.4432815  0.4433885  0.4434955  0.4436024  0.4437094  0.4438164
##      trend[949] trend[950] trend[951] trend[952] trend[953] trend[954]
## [1,]  0.4439234  0.4440303  0.4441373  0.4442443  0.4443513  0.4444582
##      trend[955] trend[956] trend[957] trend[958] trend[959] trend[960]
## [1,]  0.4445652  0.4446722  0.4447792  0.4448861  0.4449931  0.4451001
##      trend[961] trend[962] trend[963] trend[964] trend[965] trend[966]
## [1,]  0.4452071   0.445314   0.445421   0.445528   0.445635  0.4457419
##      trend[967] trend[968] trend[969] trend[970] trend[971] trend[972]
## [1,]  0.4458489  0.4459559  0.4460629  0.4461698  0.4462768  0.4463838
##      trend[973] trend[974] trend[975] trend[976] trend[977] trend[978]
## [1,]  0.4464908  0.4465977  0.4467047  0.4468117  0.4469187  0.4470256
##      trend[979] trend[980] trend[981] trend[982] trend[983] trend[984]
## [1,]  0.4471326  0.4472396  0.4473466  0.4475024  0.4476581  0.4478139
##      trend[985] trend[986] trend[987] trend[988] trend[989] trend[990]
## [1,]  0.4479697  0.4481255  0.4482813  0.4484371  0.4485929  0.4487487
##      trend[991] trend[992] trend[993] trend[994] trend[995] trend[996]
## [1,]  0.4489045  0.4490602   0.449216  0.4493718  0.4495276  0.4496834
##      trend[997] trend[998] trend[999] trend[1000] trend[1001] trend[1002]
## [1,]  0.4498392   0.449995  0.4501508   0.4503065   0.4504623   0.4506181
##      trend[1003] trend[1004] trend[1005] trend[1006] trend[1007] trend[1008]
## [1,]   0.4507739   0.4509297   0.4510855   0.4512413   0.4513971   0.4515528
##      trend[1009] trend[1010] trend[1011] trend[1012] trend[1013] trend[1014]
## [1,]   0.4517086   0.4518644   0.4520202    0.452176   0.4523318   0.4524876
##      trend[1015] trend[1016] trend[1017] trend[1018] trend[1019] trend[1020]
## [1,]   0.4526434   0.4527992   0.4529549   0.4531107   0.4532665   0.4534223
##      trend[1021] trend[1022] trend[1023] trend[1024] trend[1025] trend[1026]
## [1,]   0.4535781   0.4537339   0.4538897   0.4540455   0.4542012    0.454357
##      trend[1027] trend[1028] trend[1029] trend[1030] trend[1031] trend[1032]
## [1,]   0.4545128   0.4546686    0.454836   0.4550033   0.4551706    0.455338
##      trend[1033] trend[1034] trend[1035] trend[1036] trend[1037] trend[1038]
## [1,]   0.4555053   0.4556727     0.45584   0.4560074   0.4561747   0.4563421
##      trend[1039] trend[1040] trend[1041] trend[1042] trend[1043] trend[1044]
## [1,]   0.4565094   0.4566768   0.4568441   0.4570114   0.4571788   0.4573461
##      trend[1045] trend[1046] trend[1047] trend[1048] trend[1049] trend[1050]
## [1,]   0.4575135   0.4576808   0.4578482   0.4580155   0.4581829   0.4583502
##      trend[1051] trend[1052] trend[1053] trend[1054] trend[1055] trend[1056]
## [1,]   0.4585176   0.4586849   0.4588523   0.4590196   0.4591869   0.4593543
##      trend[1057] trend[1058] trend[1059] trend[1060] trend[1061] trend[1062]
## [1,]   0.4595216    0.459689   0.4598563   0.4600237    0.460191   0.4603584
##      trend[1063] trend[1064] trend[1065] trend[1066] trend[1067] trend[1068]
## [1,]   0.4605257   0.4606931   0.4608604   0.4610277   0.4611951   0.4613624
##      trend[1069] trend[1070] trend[1071] trend[1072] trend[1073] trend[1074]
## [1,]   0.4615298   0.4616971   0.4618645   0.4620318   0.4621992   0.4623665
##      trend[1075] trend[1076] trend[1077] trend[1078] trend[1079] trend[1080]
## [1,]   0.4625339   0.4627039   0.4628739   0.4630439   0.4632139   0.4633839
##      trend[1081] trend[1082] trend[1083] trend[1084] trend[1085] trend[1086]
## [1,]   0.4635539   0.4637239   0.4638939   0.4640639    0.464234    0.464404
##      trend[1087] trend[1088] trend[1089] trend[1090] trend[1091] trend[1092]
## [1,]    0.464574    0.464744    0.464914    0.465084    0.465254    0.465424
##      trend[1093] trend[1094] trend[1095] trend[1096] trend[1097] trend[1098]
## [1,]    0.465594    0.465764    0.465934   0.4661041   0.4662741   0.4664441
##      trend[1099] trend[1100] trend[1101] trend[1102] trend[1103] trend[1104]
## [1,]   0.4666141   0.4667841   0.4669541   0.4671241   0.4672941   0.4674641
##      trend[1105] trend[1106] trend[1107] trend[1108] trend[1109] trend[1110]
## [1,]   0.4676341   0.4678042   0.4679742   0.4681442   0.4683142   0.4684842
##      trend[1111] trend[1112] trend[1113] trend[1114] trend[1115] trend[1116]
## [1,]   0.4686542   0.4688242   0.4689942   0.4691642   0.4693342   0.4695042
##      trend[1117] trend[1118] trend[1119] trend[1120] trend[1121] trend[1122]
## [1,]   0.4696743   0.4698443   0.4700143   0.4701843   0.4703543   0.4705243
##      trend[1123] trend[1124] trend[1125] trend[1126] trend[1127] trend[1128]
## [1,]   0.4706943   0.4708643   0.4710343   0.4712043   0.4713743   0.4715444
##      trend[1129] trend[1130] trend[1131] trend[1132] trend[1133] trend[1134]
## [1,]   0.4717144   0.4718844   0.4720544   0.4722244   0.4723944   0.4725644
##      trend[1135] trend[1136] trend[1137] trend[1138] trend[1139] trend[1140]
## [1,]   0.4727344   0.4729044   0.4730744   0.4732444   0.4734145   0.4735845
##      trend[1141] trend[1142] trend[1143] trend[1144] trend[1145] trend[1146]
## [1,]   0.4737545   0.4739245   0.4740945   0.4742645   0.4744345   0.4746045
##      trend[1147] trend[1148] trend[1149] trend[1150] trend[1151] trend[1152]
## [1,]   0.4747745   0.4749445   0.4751146   0.4752846   0.4754546   0.4756246
##      trend[1153] trend[1154] trend[1155] trend[1156] trend[1157] trend[1158]
## [1,]   0.4757946   0.4759646   0.4761346   0.4763046   0.4764746   0.4766446
##      trend[1159] trend[1160] trend[1161] trend[1162] trend[1163] trend[1164]
## [1,]   0.4768146   0.4769847   0.4771547   0.4773247   0.4774947   0.4776647
##      trend[1165] trend[1166] trend[1167] trend[1168] trend[1169] trend[1170]
## [1,]   0.4778347   0.4780047   0.4781747   0.4783447   0.4784675   0.4785903
##      trend[1171] trend[1172] trend[1173] trend[1174] trend[1175] trend[1176]
## [1,]   0.4787131   0.4788359   0.4789587   0.4790815   0.4792043    0.479327
##      trend[1177] trend[1178] trend[1179] trend[1180] trend[1181] trend[1182]
## [1,]   0.4794498   0.4795726   0.4796954   0.4798182    0.479941   0.4800638
##      trend[1183] trend[1184] trend[1185] trend[1186] trend[1187] trend[1188]
## [1,]   0.4801866   0.4803094   0.4804321   0.4805549   0.4806777   0.4808005
##      trend[1189] trend[1190] trend[1191] trend[1192] trend[1193] trend[1194]
## [1,]   0.4809233   0.4810461   0.4811689   0.4812917   0.4814145   0.4815372
##      trend[1195] trend[1196] trend[1197] trend[1198] trend[1199] trend[1200]
## [1,]     0.48166   0.4817828   0.4819056   0.4820284   0.4821512    0.482274
##      trend[1201] trend[1202] trend[1203] trend[1204] trend[1205] trend[1206]
## [1,]   0.4823968   0.4825195   0.4826423   0.4827651   0.4828879   0.4830107
##      trend[1207] trend[1208] trend[1209] trend[1210] trend[1211] trend[1212]
## [1,]   0.4831335   0.4832563   0.4833791   0.4835019   0.4836246   0.4837474
##      trend[1213] trend[1214] trend[1215] trend[1216] trend[1217] trend[1218]
## [1,]   0.4838702    0.483993   0.4841158   0.4842386   0.4843614   0.4844842
##      trend[1219] trend[1220] trend[1221] trend[1222] trend[1223] trend[1224]
## [1,]    0.484607   0.4847297   0.4848525   0.4849753   0.4850981   0.4852209
##      trend[1225] trend[1226] trend[1227] trend[1228] trend[1229] trend[1230]
## [1,]   0.4853437   0.4854665   0.4855893   0.4857121   0.4858348   0.4859576
##      trend[1231] trend[1232] trend[1233] trend[1234] trend[1235] trend[1236]
## [1,]   0.4860804   0.4862032    0.486326   0.4864488   0.4865716   0.4866944
##      trend[1237] trend[1238] trend[1239] trend[1240] trend[1241] trend[1242]
## [1,]   0.4868172   0.4869399   0.4870627   0.4871855   0.4873083   0.4874311
##      trend[1243] trend[1244] trend[1245] trend[1246] trend[1247] trend[1248]
## [1,]   0.4875539   0.4876767   0.4877995   0.4879223    0.488045   0.4881678
##      trend[1249] trend[1250] trend[1251] trend[1252] trend[1253] trend[1254]
## [1,]   0.4882906   0.4884134   0.4885362    0.488659   0.4887818   0.4889046
##      trend[1255] trend[1256] trend[1257] trend[1258] trend[1259] trend[1260]
## [1,]   0.4890274   0.4891501   0.4892729   0.4893957   0.4895185   0.4896413
##      trend[1261] trend[1262] trend[1263] trend[1264] trend[1265] trend[1266]
## [1,]   0.4897641   0.4898869   0.4900097   0.4901325   0.4902552    0.490378
##      trend[1267] trend[1268] trend[1269] trend[1270] trend[1271] trend[1272]
## [1,]   0.4905008   0.4906236   0.4907464   0.4908692    0.490992   0.4911148
##      trend[1273] trend[1274] trend[1275] trend[1276] trend[1277] trend[1278]
## [1,]   0.4912376   0.4913603   0.4914831   0.4916059   0.4917287   0.4918515
##      trend[1279] trend[1280] trend[1281] trend[1282] trend[1283] trend[1284]
## [1,]   0.4919743   0.4920971   0.4922199   0.4923427   0.4924654   0.4925882
##      trend[1285] trend[1286] trend[1287] trend[1288] trend[1289] trend[1290]
## [1,]    0.492711   0.4928338   0.4929566   0.4930794   0.4932022    0.493325
##      trend[1291] trend[1292] trend[1293] trend[1294] trend[1295] trend[1296]
## [1,]   0.4934478   0.4935705   0.4936933   0.4938161   0.4939389   0.4940617
##      trend[1297] trend[1298] trend[1299] trend[1300] trend[1301] trend[1302]
## [1,]   0.4941845   0.4943073   0.4944301   0.4945529   0.4946756   0.4947984
##      trend[1303] trend[1304] trend[1305] trend[1306] trend[1307] trend[1308]
## [1,]   0.4949212    0.495044   0.4951668   0.4952896   0.4954124   0.4955352
##      trend[1309] trend[1310] trend[1311] trend[1312] trend[1313] trend[1314]
## [1,]    0.495658   0.4957807   0.4959035   0.4960263   0.4961491   0.4962719
##      trend[1315] trend[1316] trend[1317] trend[1318] trend[1319] trend[1320]
## [1,]   0.4963947   0.4965175   0.4966403    0.496763   0.4968858   0.4970086
##      trend[1321] trend[1322] trend[1323] trend[1324] trend[1325] trend[1326]
## [1,]   0.4971314   0.4972542    0.497377   0.4974998   0.4976226   0.4977454
##      trend[1327] trend[1328] trend[1329] trend[1330] trend[1331] trend[1332]
## [1,]   0.4978681   0.4979909   0.4981137   0.4982365   0.4983593   0.4984821
##      trend[1333] trend[1334] trend[1335] trend[1336] trend[1337] trend[1338]
## [1,]   0.4986049   0.4987277   0.4988505   0.4989732    0.499096   0.4992188
##      trend[1339] trend[1340] trend[1341] trend[1342] trend[1343] trend[1344]
## [1,]   0.4993416   0.4994644   0.4995872     0.49971   0.4998328   0.4999556
##      trend[1345] trend[1346] trend[1347] trend[1348] trend[1349] trend[1350]
## [1,]   0.5000783   0.5002011   0.5003239   0.5004467   0.5005695   0.5006923
##      trend[1351] trend[1352] trend[1353] trend[1354] trend[1355] trend[1356]
## [1,]   0.5008151   0.5009379   0.5010607   0.5011834   0.5013062    0.501429
##      trend[1357] trend[1358] trend[1359] trend[1360] trend[1361] trend[1362]
## [1,]   0.5015518   0.5016746   0.5017974   0.5019202    0.502043   0.5021658
##      trend[1363] trend[1364] trend[1365] trend[1366] trend[1367] trend[1368]
## [1,]   0.5022885   0.5024113   0.5025341   0.5026569   0.5027797   0.5029025
##      trend[1369] trend[1370] trend[1371] trend[1372] trend[1373] trend[1374]
## [1,]   0.5030253   0.5031481   0.5032709   0.5033936   0.5035164   0.5036392
##      trend[1375] trend[1376] trend[1377] trend[1378] trend[1379] trend[1380]
## [1,]    0.503762   0.5038848   0.5040076   0.5041304   0.5042532    0.504376
##      trend[1381] trend[1382] trend[1383] trend[1384] trend[1385] trend[1386]
## [1,]   0.5044987   0.5046215   0.5047443   0.5048671   0.5049899   0.5051127
##      trend[1387] trend[1388] trend[1389] trend[1390] trend[1391] trend[1392]
## [1,]   0.5052355   0.5053583   0.5054811   0.5056038   0.5057266   0.5058494
##      trend[1393] trend[1394] trend[1395] trend[1396] trend[1397] trend[1398]
## [1,]   0.5059722    0.506095   0.5062178   0.5063406   0.5064634   0.5065862
##      trend[1399] trend[1400] trend[1401] trend[1402] trend[1403] trend[1404]
## [1,]   0.5067089   0.5068317   0.5069545   0.5070773   0.5072001   0.5073229
##      trend[1405] trend[1406] trend[1407] trend[1408] trend[1409] trend[1410]
## [1,]   0.5074457   0.5075685   0.5076913    0.507814   0.5079368   0.5080596
##      trend[1411] trend[1412] trend[1413] trend[1414] trend[1415] trend[1416]
## [1,]   0.5081824   0.5083052    0.508428   0.5085508   0.5086736   0.5087964
##      trend[1417] trend[1418] trend[1419] trend[1420] trend[1421] trend[1422]
## [1,]   0.5089191   0.5090419   0.5091647   0.5092875   0.5094103   0.5095331
##      trend[1423] trend[1424] trend[1425] trend[1426] trend[1427] trend[1428]
## [1,]   0.5096559   0.5097787   0.5099015   0.5100242    0.510147   0.5102698
##      trend[1429] trend[1430] trend[1431] trend[1432] trend[1433] trend[1434]
## [1,]   0.5103926   0.5105154   0.5106382    0.510761   0.5108838   0.5110065
##      trend[1435] trend[1436] trend[1437] trend[1438] trend[1439] trend[1440]
## [1,]   0.5111293   0.5112521   0.5113749   0.5114977   0.5116205   0.5117433
##      trend[1441] trend[1442] trend[1443] trend[1444] trend[1445] trend[1446]
## [1,]   0.5118661   0.5119889   0.5121116   0.5122344   0.5123572     0.51248
##      trend[1447] trend[1448] trend[1449] trend[1450] trend[1451] trend[1452]
## [1,]   0.5126028   0.5127256   0.5128484   0.5129712    0.513094   0.5132167
##      trend[1453] trend[1454] trend[1455] trend[1456] trend[1457] trend[1458]
## [1,]   0.5133395   0.5134623   0.5135851   0.5137079   0.5138307   0.5139535
##      trend[1459] trend[1460] trend[1461]
## [1,]   0.5140763   0.5141991   0.5143218
## 
## 
## $params
## $params$k
## [1] -0.3399185
## 
## $params$m
## [1] 0.3551693
## 
## $params$delta
##              [,1]         [,2]     [,3]      [,4]      [,5]         [,6]
## [1,] 7.557253e-08 3.483415e-08 0.268866 0.4799589 0.2004927 6.476051e-08
##              [,7]       [,8]       [,9]         [,10]     [,11]        [,12]
## [1,] 5.903609e-08 -0.2108516 -0.2755958 -1.215397e-07 4.155e-08 2.488461e-07
##              [,13]        [,14]       [,15]         [,16]         [,17]
## [1,] -1.266203e-08 -0.003357057 -0.03749413 -1.522682e-08 -6.884554e-08
##            [,18]      [,19]      [,20]     [,21]      [,22]       [,23]
## [1,] 0.007239539 0.02767627 0.03916694 0.0712668 0.01687457 0.003888608
##             [,24]       [,25]
## [1,] 1.302859e-07 -0.06894206
## 
## $params$sigma_obs
## [1] 0.02704036
## 
## $params$beta
##             [,1]       [,2]        [,3]         [,4]        [,5]        [,6]
## [1,] -0.01503878 -0.1395354 -0.02416547 -0.007901517 -0.01777479 -0.02432104
##             [,7]         [,8]        [,9]      [,10]      [,11]       [,12]
## [1,] 0.007693029 -0.008147217 0.006676297 -0.0118898 0.01535229 0.003032079
##            [,13]       [,14]       [,15]       [,16]        [,17]      [,18]
## [1,] 0.003252465 0.009647003 0.004167203 0.005074982 -0.007422047 0.00594854
##             [,19]         [,20]      [,21]       [,22]       [,23]        [,24]
## [1,] -0.004875237 -0.0004564492 0.07696883 -0.00257081 -0.04462161 -0.009995736
##           [,25]       [,26]         [,27]     [,28]         [,29]     [,30]
## [1,] 0.04729456 0.006687925 -5.405959e-11 0.0382359 -1.081192e-10 0.0382359
##              [,31]     [,32]         [,33]     [,34]
## [1,] -2.690668e-11 0.0382359 -2.162384e-10 0.0382359
## 
## $params$trend
##    [1] 0.3551693 0.3549365 0.3547037 0.3544709 0.3542380 0.3540052 0.3537724
##    [8] 0.3535396 0.3533068 0.3530739 0.3528411 0.3526083 0.3523755 0.3521427
##   [15] 0.3519098 0.3516770 0.3514442 0.3512114 0.3509785 0.3507457 0.3505129
##   [22] 0.3502801 0.3500473 0.3498144 0.3495816 0.3493488 0.3491160 0.3488832
##   [29] 0.3486503 0.3484175 0.3481847 0.3479519 0.3477191 0.3474862 0.3472534
##   [36] 0.3470206 0.3467878 0.3465550 0.3463221 0.3460893 0.3458565 0.3456237
##   [43] 0.3453908 0.3451580 0.3449252 0.3446924 0.3444596 0.3442267 0.3439939
##   [50] 0.3437611 0.3435283 0.3432955 0.3430626 0.3428298 0.3425970 0.3423642
##   [57] 0.3421314 0.3418985 0.3416657 0.3414329 0.3412001 0.3409673 0.3407344
##   [64] 0.3405016 0.3402688 0.3400360 0.3398031 0.3395703 0.3393375 0.3391047
##   [71] 0.3388719 0.3386390 0.3384062 0.3381734 0.3379406 0.3377078 0.3374749
##   [78] 0.3372421 0.3370093 0.3367765 0.3365437 0.3363108 0.3360780 0.3358452
##   [85] 0.3356124 0.3353796 0.3351467 0.3349139 0.3346811 0.3344483 0.3342154
##   [92] 0.3339826 0.3337498 0.3335170 0.3332842 0.3330513 0.3328185 0.3325857
##   [99] 0.3323529 0.3321201 0.3318872 0.3316544 0.3314216 0.3311888 0.3309560
##  [106] 0.3307231 0.3304903 0.3302575 0.3300247 0.3297919 0.3295590 0.3293262
##  [113] 0.3290934 0.3288606 0.3286277 0.3283949 0.3281621 0.3279293 0.3276965
##  [120] 0.3274636 0.3272308 0.3269980 0.3267652 0.3265324 0.3262995 0.3260667
##  [127] 0.3258339 0.3256011 0.3253683 0.3251354 0.3249026 0.3246698 0.3244370
##  [134] 0.3242042 0.3239713 0.3237385 0.3235057 0.3232729 0.3230400 0.3228072
##  [141] 0.3225744 0.3225257 0.3224771 0.3224284 0.3223797 0.3223311 0.3222824
##  [148] 0.3222337 0.3221851 0.3221364 0.3220877 0.3220391 0.3219904 0.3219417
##  [155] 0.3218931 0.3218444 0.3217957 0.3217471 0.3216984 0.3216498 0.3216011
##  [162] 0.3215524 0.3215038 0.3214551 0.3214064 0.3213578 0.3213091 0.3212604
##  [169] 0.3212118 0.3211631 0.3211144 0.3210658 0.3210171 0.3209684 0.3209198
##  [176] 0.3208711 0.3208224 0.3207738 0.3207251 0.3206764 0.3206278 0.3205791
##  [183] 0.3205304 0.3204818 0.3204331 0.3203844 0.3203358 0.3202871 0.3205672
##  [190] 0.3208472 0.3211273 0.3214074 0.3216875 0.3219675 0.3222476 0.3225277
##  [197] 0.3228078 0.3230878 0.3233679 0.3236480 0.3239280 0.3242081 0.3244882
##  [204] 0.3247683 0.3250483 0.3253284 0.3256085 0.3258886 0.3261686 0.3264487
##  [211] 0.3267288 0.3270089 0.3272889 0.3275690 0.3278491 0.3281291 0.3284092
##  [218] 0.3286893 0.3289694 0.3292494 0.3295295 0.3298096 0.3300897 0.3303697
##  [225] 0.3306498 0.3309299 0.3312099 0.3314900 0.3317701 0.3320502 0.3323302
##  [232] 0.3326103 0.3328904 0.3331705 0.3335879 0.3340052 0.3344226 0.3348400
##  [239] 0.3352574 0.3356748 0.3360922 0.3365096 0.3369270 0.3373444 0.3377618
##  [246] 0.3381792 0.3385966 0.3390140 0.3394314 0.3398488 0.3402662 0.3406836
##  [253] 0.3411010 0.3415184 0.3419358 0.3423532 0.3427706 0.3431880 0.3436054
##  [260] 0.3440228 0.3444402 0.3448576 0.3452750 0.3456924 0.3461098 0.3465272
##  [267] 0.3469445 0.3473619 0.3477793 0.3481967 0.3486141 0.3490315 0.3494489
##  [274] 0.3498663 0.3502837 0.3507011 0.3511185 0.3515359 0.3519533 0.3523707
##  [281] 0.3527881 0.3532055 0.3536229 0.3540403 0.3544577 0.3548751 0.3552925
##  [288] 0.3557099 0.3561273 0.3565447 0.3569621 0.3573795 0.3577969 0.3582143
##  [295] 0.3586317 0.3590491 0.3594665 0.3598838 0.3603012 0.3607186 0.3611360
##  [302] 0.3615534 0.3619708 0.3623882 0.3628056 0.3632230 0.3636404 0.3640578
##  [309] 0.3644752 0.3648926 0.3653100 0.3657274 0.3661448 0.3665622 0.3669796
##  [316] 0.3673970 0.3678144 0.3682318 0.3686492 0.3690666 0.3694840 0.3699014
##  [323] 0.3703188 0.3707362 0.3711536 0.3715710 0.3719884 0.3724057 0.3728231
##  [330] 0.3732405 0.3736579 0.3740753 0.3744927 0.3749101 0.3753275 0.3757449
##  [337] 0.3761623 0.3765797 0.3769971 0.3774145 0.3778319 0.3782493 0.3786667
##  [344] 0.3790841 0.3795015 0.3799189 0.3803363 0.3807537 0.3811711 0.3815885
##  [351] 0.3820059 0.3824233 0.3828407 0.3832581 0.3836755 0.3840929 0.3845103
##  [358] 0.3849277 0.3853451 0.3857624 0.3861798 0.3865972 0.3870146 0.3874320
##  [365] 0.3878494 0.3882668 0.3886842 0.3891016 0.3895190 0.3899364 0.3903538
##  [372] 0.3907712 0.3911886 0.3916060 0.3918790 0.3921520 0.3924249 0.3926979
##  [379] 0.3929709 0.3932439 0.3935168 0.3937898 0.3940628 0.3943358 0.3946088
##  [386] 0.3948817 0.3951547 0.3954277 0.3957007 0.3959736 0.3962466 0.3965196
##  [393] 0.3967926 0.3970656 0.3973385 0.3976115 0.3978845 0.3981575 0.3984305
##  [400] 0.3987034 0.3989764 0.3992494 0.3995224 0.3997953 0.4000683 0.4003413
##  [407] 0.4006143 0.4008873 0.4011602 0.4014332 0.4017062 0.4019792 0.4022521
##  [414] 0.4025251 0.4027981 0.4030711 0.4033441 0.4036170 0.4038900 0.4041630
##  [421] 0.4044360 0.4045202 0.4046044 0.4046886 0.4047728 0.4048570 0.4049412
##  [428] 0.4050255 0.4051097 0.4051939 0.4052781 0.4053623 0.4054465 0.4055307
##  [435] 0.4056150 0.4056992 0.4057834 0.4058676 0.4059518 0.4060360 0.4061202
##  [442] 0.4062045 0.4062887 0.4063729 0.4064571 0.4065413 0.4066255 0.4067097
##  [449] 0.4067939 0.4068782 0.4069624 0.4070466 0.4071308 0.4072150 0.4072992
##  [456] 0.4073834 0.4074677 0.4075519 0.4076361 0.4077203 0.4078045 0.4078887
##  [463] 0.4079729 0.4080572 0.4081414 0.4082256 0.4083098 0.4083940 0.4084782
##  [470] 0.4085624 0.4086466 0.4087309 0.4088151 0.4088993 0.4089835 0.4090677
##  [477] 0.4091519 0.4092361 0.4093204 0.4094046 0.4094888 0.4095730 0.4096572
##  [484] 0.4097414 0.4098256 0.4099099 0.4099941 0.4100783 0.4101625 0.4102467
##  [491] 0.4103309 0.4104151 0.4104993 0.4105836 0.4106678 0.4107520 0.4108362
##  [498] 0.4109204 0.4110046 0.4110888 0.4111731 0.4112573 0.4113415 0.4114257
##  [505] 0.4115099 0.4115941 0.4116783 0.4117626 0.4118468 0.4119310 0.4120152
##  [512] 0.4120994 0.4121836 0.4122678 0.4123520 0.4124363 0.4125205 0.4126047
##  [519] 0.4126889 0.4127731 0.4128573 0.4129415 0.4130258 0.4131100 0.4131942
##  [526] 0.4132784 0.4133626 0.4134468 0.4135310 0.4136153 0.4136995 0.4137837
##  [533] 0.4138679 0.4139521 0.4140363 0.4141205 0.4142047 0.4142890 0.4143732
##  [540] 0.4144574 0.4145416 0.4146258 0.4147100 0.4147942 0.4148785 0.4149627
##  [547] 0.4150469 0.4151311 0.4152153 0.4152995 0.4153837 0.4154679 0.4155522
##  [554] 0.4156364 0.4157206 0.4158048 0.4158890 0.4159732 0.4160574 0.4161417
##  [561] 0.4162259 0.4163101 0.4163943 0.4164785 0.4165627 0.4166469 0.4167312
##  [568] 0.4168154 0.4168996 0.4169838 0.4170680 0.4171522 0.4172364 0.4173207
##  [575] 0.4174049 0.4174891 0.4175733 0.4176575 0.4177417 0.4178259 0.4179101
##  [582] 0.4179944 0.4180786 0.4181628 0.4182470 0.4183312 0.4184154 0.4184996
##  [589] 0.4185839 0.4186681 0.4187523 0.4188365 0.4189207 0.4190049 0.4190891
##  [596] 0.4191734 0.4192576 0.4193418 0.4194260 0.4195102 0.4195944 0.4196786
##  [603] 0.4197629 0.4198471 0.4199313 0.4200155 0.4200997 0.4201839 0.4202681
##  [610] 0.4203523 0.4204366 0.4205208 0.4206050 0.4206892 0.4207734 0.4208576
##  [617] 0.4209418 0.4210261 0.4211103 0.4211945 0.4212787 0.4213629 0.4214471
##  [624] 0.4215313 0.4216156 0.4216998 0.4217840 0.4218682 0.4219524 0.4220366
##  [631] 0.4221208 0.4222051 0.4222893 0.4223735 0.4224577 0.4225419 0.4226261
##  [638] 0.4227103 0.4227945 0.4228788 0.4229630 0.4230472 0.4231314 0.4232156
##  [645] 0.4232998 0.4233840 0.4234683 0.4235525 0.4236367 0.4237209 0.4238051
##  [652] 0.4238893 0.4239735 0.4240578 0.4241420 0.4242239 0.4243058 0.4243877
##  [659] 0.4244696 0.4245515 0.4246335 0.4247154 0.4247973 0.4248792 0.4249611
##  [666] 0.4250430 0.4251249 0.4252069 0.4252888 0.4253707 0.4254526 0.4255345
##  [673] 0.4256164 0.4256983 0.4257803 0.4258622 0.4259441 0.4260260 0.4261079
##  [680] 0.4261898 0.4262717 0.4263537 0.4264356 0.4265175 0.4265994 0.4266813
##  [687] 0.4267632 0.4268451 0.4269271 0.4270090 0.4270909 0.4271728 0.4272547
##  [694] 0.4273366 0.4274185 0.4275005 0.4275824 0.4276643 0.4277462 0.4278281
##  [701] 0.4279100 0.4279663 0.4280225 0.4280787 0.4281350 0.4281912 0.4282474
##  [708] 0.4283037 0.4283599 0.4284161 0.4284724 0.4285286 0.4285848 0.4286411
##  [715] 0.4286973 0.4287535 0.4288098 0.4288660 0.4289222 0.4289785 0.4290347
##  [722] 0.4290909 0.4291472 0.4292034 0.4292596 0.4293159 0.4293721 0.4294283
##  [729] 0.4294846 0.4295408 0.4295970 0.4296533 0.4297095 0.4297657 0.4298220
##  [736] 0.4298782 0.4299344 0.4299907 0.4300469 0.4301031 0.4301594 0.4302156
##  [743] 0.4302718 0.4303281 0.4303843 0.4304405 0.4304968 0.4305530 0.4306092
##  [750] 0.4306655 0.4307217 0.4307779 0.4308342 0.4308904 0.4309466 0.4310029
##  [757] 0.4310591 0.4311153 0.4311716 0.4312278 0.4312840 0.4313403 0.4313965
##  [764] 0.4314527 0.4315090 0.4315652 0.4316214 0.4316777 0.4317339 0.4317901
##  [771] 0.4318464 0.4319026 0.4319588 0.4320151 0.4320713 0.4321275 0.4321838
##  [778] 0.4322400 0.4322962 0.4323525 0.4324087 0.4324649 0.4325212 0.4325774
##  [785] 0.4326336 0.4326899 0.4327461 0.4328023 0.4328586 0.4329148 0.4329710
##  [792] 0.4330273 0.4330835 0.4331397 0.4331960 0.4332522 0.4333084 0.4333647
##  [799] 0.4334209 0.4334771 0.4335334 0.4335896 0.4336458 0.4337021 0.4337583
##  [806] 0.4338145 0.4338708 0.4339270 0.4339832 0.4340395 0.4340957 0.4341520
##  [813] 0.4342082 0.4342644 0.4343207 0.4343769 0.4344331 0.4344894 0.4345456
##  [820] 0.4346018 0.4346581 0.4347143 0.4347705 0.4348268 0.4348830 0.4349392
##  [827] 0.4349955 0.4350517 0.4351079 0.4351642 0.4352204 0.4352766 0.4353329
##  [834] 0.4353891 0.4354453 0.4355016 0.4355578 0.4356140 0.4356703 0.4357265
##  [841] 0.4357827 0.4358439 0.4359051 0.4359663 0.4360275 0.4360887 0.4361499
##  [848] 0.4362111 0.4362723 0.4363334 0.4363946 0.4364558 0.4365170 0.4365782
##  [855] 0.4366394 0.4367006 0.4367618 0.4368230 0.4368842 0.4369454 0.4370066
##  [862] 0.4370678 0.4371289 0.4371901 0.4372513 0.4373125 0.4373737 0.4374349
##  [869] 0.4374961 0.4375573 0.4376185 0.4376797 0.4377409 0.4378021 0.4378632
##  [876] 0.4379244 0.4379856 0.4380468 0.4381080 0.4381692 0.4382304 0.4382916
##  [883] 0.4383528 0.4384140 0.4384752 0.4385364 0.4385976 0.4386587 0.4387389
##  [890] 0.4388190 0.4388992 0.4389793 0.4390595 0.4391396 0.4392198 0.4392999
##  [897] 0.4393801 0.4394602 0.4395404 0.4396205 0.4397007 0.4397808 0.4398610
##  [904] 0.4399411 0.4400213 0.4401014 0.4401816 0.4402617 0.4403419 0.4404220
##  [911] 0.4405022 0.4405823 0.4406625 0.4407426 0.4408228 0.4409029 0.4409830
##  [918] 0.4410632 0.4411433 0.4412235 0.4413036 0.4413838 0.4414639 0.4415441
##  [925] 0.4416242 0.4417044 0.4417845 0.4418647 0.4419448 0.4420250 0.4421051
##  [932] 0.4421853 0.4422654 0.4423456 0.4424257 0.4425327 0.4426397 0.4427466
##  [939] 0.4428536 0.4429606 0.4430676 0.4431745 0.4432815 0.4433885 0.4434955
##  [946] 0.4436024 0.4437094 0.4438164 0.4439234 0.4440303 0.4441373 0.4442443
##  [953] 0.4443513 0.4444582 0.4445652 0.4446722 0.4447792 0.4448861 0.4449931
##  [960] 0.4451001 0.4452071 0.4453140 0.4454210 0.4455280 0.4456350 0.4457419
##  [967] 0.4458489 0.4459559 0.4460629 0.4461698 0.4462768 0.4463838 0.4464908
##  [974] 0.4465977 0.4467047 0.4468117 0.4469187 0.4470256 0.4471326 0.4472396
##  [981] 0.4473466 0.4475024 0.4476581 0.4478139 0.4479697 0.4481255 0.4482813
##  [988] 0.4484371 0.4485929 0.4487487 0.4489045 0.4490602 0.4492160 0.4493718
##  [995] 0.4495276 0.4496834 0.4498392 0.4499950 0.4501508 0.4503065 0.4504623
## [1002] 0.4506181 0.4507739 0.4509297 0.4510855 0.4512413 0.4513971 0.4515528
## [1009] 0.4517086 0.4518644 0.4520202 0.4521760 0.4523318 0.4524876 0.4526434
## [1016] 0.4527992 0.4529549 0.4531107 0.4532665 0.4534223 0.4535781 0.4537339
## [1023] 0.4538897 0.4540455 0.4542012 0.4543570 0.4545128 0.4546686 0.4548360
## [1030] 0.4550033 0.4551706 0.4553380 0.4555053 0.4556727 0.4558400 0.4560074
## [1037] 0.4561747 0.4563421 0.4565094 0.4566768 0.4568441 0.4570114 0.4571788
## [1044] 0.4573461 0.4575135 0.4576808 0.4578482 0.4580155 0.4581829 0.4583502
## [1051] 0.4585176 0.4586849 0.4588523 0.4590196 0.4591869 0.4593543 0.4595216
## [1058] 0.4596890 0.4598563 0.4600237 0.4601910 0.4603584 0.4605257 0.4606931
## [1065] 0.4608604 0.4610277 0.4611951 0.4613624 0.4615298 0.4616971 0.4618645
## [1072] 0.4620318 0.4621992 0.4623665 0.4625339 0.4627039 0.4628739 0.4630439
## [1079] 0.4632139 0.4633839 0.4635539 0.4637239 0.4638939 0.4640639 0.4642340
## [1086] 0.4644040 0.4645740 0.4647440 0.4649140 0.4650840 0.4652540 0.4654240
## [1093] 0.4655940 0.4657640 0.4659340 0.4661041 0.4662741 0.4664441 0.4666141
## [1100] 0.4667841 0.4669541 0.4671241 0.4672941 0.4674641 0.4676341 0.4678042
## [1107] 0.4679742 0.4681442 0.4683142 0.4684842 0.4686542 0.4688242 0.4689942
## [1114] 0.4691642 0.4693342 0.4695042 0.4696743 0.4698443 0.4700143 0.4701843
## [1121] 0.4703543 0.4705243 0.4706943 0.4708643 0.4710343 0.4712043 0.4713743
## [1128] 0.4715444 0.4717144 0.4718844 0.4720544 0.4722244 0.4723944 0.4725644
## [1135] 0.4727344 0.4729044 0.4730744 0.4732444 0.4734145 0.4735845 0.4737545
## [1142] 0.4739245 0.4740945 0.4742645 0.4744345 0.4746045 0.4747745 0.4749445
## [1149] 0.4751146 0.4752846 0.4754546 0.4756246 0.4757946 0.4759646 0.4761346
## [1156] 0.4763046 0.4764746 0.4766446 0.4768146 0.4769847 0.4771547 0.4773247
## [1163] 0.4774947 0.4776647 0.4778347 0.4780047 0.4781747 0.4783447 0.4784675
## [1170] 0.4785903 0.4787131 0.4788359 0.4789587 0.4790815 0.4792043 0.4793270
## [1177] 0.4794498 0.4795726 0.4796954 0.4798182 0.4799410 0.4800638 0.4801866
## [1184] 0.4803094 0.4804321 0.4805549 0.4806777 0.4808005 0.4809233 0.4810461
## [1191] 0.4811689 0.4812917 0.4814145 0.4815372 0.4816600 0.4817828 0.4819056
## [1198] 0.4820284 0.4821512 0.4822740 0.4823968 0.4825195 0.4826423 0.4827651
## [1205] 0.4828879 0.4830107 0.4831335 0.4832563 0.4833791 0.4835019 0.4836246
## [1212] 0.4837474 0.4838702 0.4839930 0.4841158 0.4842386 0.4843614 0.4844842
## [1219] 0.4846070 0.4847297 0.4848525 0.4849753 0.4850981 0.4852209 0.4853437
## [1226] 0.4854665 0.4855893 0.4857121 0.4858348 0.4859576 0.4860804 0.4862032
## [1233] 0.4863260 0.4864488 0.4865716 0.4866944 0.4868172 0.4869399 0.4870627
## [1240] 0.4871855 0.4873083 0.4874311 0.4875539 0.4876767 0.4877995 0.4879223
## [1247] 0.4880450 0.4881678 0.4882906 0.4884134 0.4885362 0.4886590 0.4887818
## [1254] 0.4889046 0.4890274 0.4891501 0.4892729 0.4893957 0.4895185 0.4896413
## [1261] 0.4897641 0.4898869 0.4900097 0.4901325 0.4902552 0.4903780 0.4905008
## [1268] 0.4906236 0.4907464 0.4908692 0.4909920 0.4911148 0.4912376 0.4913603
## [1275] 0.4914831 0.4916059 0.4917287 0.4918515 0.4919743 0.4920971 0.4922199
## [1282] 0.4923427 0.4924654 0.4925882 0.4927110 0.4928338 0.4929566 0.4930794
## [1289] 0.4932022 0.4933250 0.4934478 0.4935705 0.4936933 0.4938161 0.4939389
## [1296] 0.4940617 0.4941845 0.4943073 0.4944301 0.4945529 0.4946756 0.4947984
## [1303] 0.4949212 0.4950440 0.4951668 0.4952896 0.4954124 0.4955352 0.4956580
## [1310] 0.4957807 0.4959035 0.4960263 0.4961491 0.4962719 0.4963947 0.4965175
## [1317] 0.4966403 0.4967630 0.4968858 0.4970086 0.4971314 0.4972542 0.4973770
## [1324] 0.4974998 0.4976226 0.4977454 0.4978681 0.4979909 0.4981137 0.4982365
## [1331] 0.4983593 0.4984821 0.4986049 0.4987277 0.4988505 0.4989732 0.4990960
## [1338] 0.4992188 0.4993416 0.4994644 0.4995872 0.4997100 0.4998328 0.4999556
## [1345] 0.5000783 0.5002011 0.5003239 0.5004467 0.5005695 0.5006923 0.5008151
## [1352] 0.5009379 0.5010607 0.5011834 0.5013062 0.5014290 0.5015518 0.5016746
## [1359] 0.5017974 0.5019202 0.5020430 0.5021658 0.5022885 0.5024113 0.5025341
## [1366] 0.5026569 0.5027797 0.5029025 0.5030253 0.5031481 0.5032709 0.5033936
## [1373] 0.5035164 0.5036392 0.5037620 0.5038848 0.5040076 0.5041304 0.5042532
## [1380] 0.5043760 0.5044987 0.5046215 0.5047443 0.5048671 0.5049899 0.5051127
## [1387] 0.5052355 0.5053583 0.5054811 0.5056038 0.5057266 0.5058494 0.5059722
## [1394] 0.5060950 0.5062178 0.5063406 0.5064634 0.5065862 0.5067089 0.5068317
## [1401] 0.5069545 0.5070773 0.5072001 0.5073229 0.5074457 0.5075685 0.5076913
## [1408] 0.5078140 0.5079368 0.5080596 0.5081824 0.5083052 0.5084280 0.5085508
## [1415] 0.5086736 0.5087964 0.5089191 0.5090419 0.5091647 0.5092875 0.5094103
## [1422] 0.5095331 0.5096559 0.5097787 0.5099015 0.5100242 0.5101470 0.5102698
## [1429] 0.5103926 0.5105154 0.5106382 0.5107610 0.5108838 0.5110065 0.5111293
## [1436] 0.5112521 0.5113749 0.5114977 0.5116205 0.5117433 0.5118661 0.5119889
## [1443] 0.5121116 0.5122344 0.5123572 0.5124800 0.5126028 0.5127256 0.5128484
## [1450] 0.5129712 0.5130940 0.5132167 0.5133395 0.5134623 0.5135851 0.5137079
## [1457] 0.5138307 0.5139535 0.5140763 0.5141991 0.5143218
## 
## 
## $history
## # A tibble: 1,461 × 5
##    ds                      y floor        t y_scaled
##    <dttm>              <dbl> <dbl>    <dbl>    <dbl>
##  1 2013-01-01 00:00:00  1588     0 0           0.317
##  2 2013-01-02 00:00:00  1538     0 0.000685    0.307
##  3 2013-01-03 00:00:00  1635     0 0.00137     0.327
##  4 2013-01-04 00:00:00  1741     0 0.00205     0.348
##  5 2013-01-05 00:00:00  1887     0 0.00274     0.377
##  6 2013-01-06 00:00:00  1956     0 0.00342     0.391
##  7 2013-01-07 00:00:00  1313     0 0.00411     0.262
##  8 2013-01-08 00:00:00  1538     0 0.00479     0.307
##  9 2013-01-09 00:00:00  1633     0 0.00548     0.326
## 10 2013-01-10 00:00:00  1677     0 0.00616     0.335
## # ℹ 1,451 more rows
## 
## $history.dates
##    [1] "2013-01-01 GMT" "2013-01-02 GMT" "2013-01-03 GMT" "2013-01-04 GMT"
##    [5] "2013-01-05 GMT" "2013-01-06 GMT" "2013-01-07 GMT" "2013-01-08 GMT"
##    [9] "2013-01-09 GMT" "2013-01-10 GMT" "2013-01-11 GMT" "2013-01-12 GMT"
##   [13] "2013-01-13 GMT" "2013-01-14 GMT" "2013-01-15 GMT" "2013-01-16 GMT"
##   [17] "2013-01-17 GMT" "2013-01-18 GMT" "2013-01-19 GMT" "2013-01-20 GMT"
##   [21] "2013-01-21 GMT" "2013-01-22 GMT" "2013-01-23 GMT" "2013-01-24 GMT"
##   [25] "2013-01-25 GMT" "2013-01-26 GMT" "2013-01-27 GMT" "2013-01-28 GMT"
##   [29] "2013-01-29 GMT" "2013-01-30 GMT" "2013-01-31 GMT" "2013-02-01 GMT"
##   [33] "2013-02-02 GMT" "2013-02-03 GMT" "2013-02-04 GMT" "2013-02-05 GMT"
##   [37] "2013-02-06 GMT" "2013-02-07 GMT" "2013-02-08 GMT" "2013-02-09 GMT"
##   [41] "2013-02-10 GMT" "2013-02-11 GMT" "2013-02-12 GMT" "2013-02-13 GMT"
##   [45] "2013-02-14 GMT" "2013-02-15 GMT" "2013-02-16 GMT" "2013-02-17 GMT"
##   [49] "2013-02-18 GMT" "2013-02-19 GMT" "2013-02-20 GMT" "2013-02-21 GMT"
##   [53] "2013-02-22 GMT" "2013-02-23 GMT" "2013-02-24 GMT" "2013-02-25 GMT"
##   [57] "2013-02-26 GMT" "2013-02-27 GMT" "2013-02-28 GMT" "2013-03-01 GMT"
##   [61] "2013-03-02 GMT" "2013-03-03 GMT" "2013-03-04 GMT" "2013-03-05 GMT"
##   [65] "2013-03-06 GMT" "2013-03-07 GMT" "2013-03-08 GMT" "2013-03-09 GMT"
##   [69] "2013-03-10 GMT" "2013-03-11 GMT" "2013-03-12 GMT" "2013-03-13 GMT"
##   [73] "2013-03-14 GMT" "2013-03-15 GMT" "2013-03-16 GMT" "2013-03-17 GMT"
##   [77] "2013-03-18 GMT" "2013-03-19 GMT" "2013-03-20 GMT" "2013-03-21 GMT"
##   [81] "2013-03-22 GMT" "2013-03-23 GMT" "2013-03-24 GMT" "2013-03-25 GMT"
##   [85] "2013-03-26 GMT" "2013-03-27 GMT" "2013-03-28 GMT" "2013-03-29 GMT"
##   [89] "2013-03-30 GMT" "2013-03-31 GMT" "2013-04-01 GMT" "2013-04-02 GMT"
##   [93] "2013-04-03 GMT" "2013-04-04 GMT" "2013-04-05 GMT" "2013-04-06 GMT"
##   [97] "2013-04-07 GMT" "2013-04-08 GMT" "2013-04-09 GMT" "2013-04-10 GMT"
##  [101] "2013-04-11 GMT" "2013-04-12 GMT" "2013-04-13 GMT" "2013-04-14 GMT"
##  [105] "2013-04-15 GMT" "2013-04-16 GMT" "2013-04-17 GMT" "2013-04-18 GMT"
##  [109] "2013-04-19 GMT" "2013-04-20 GMT" "2013-04-21 GMT" "2013-04-22 GMT"
##  [113] "2013-04-23 GMT" "2013-04-24 GMT" "2013-04-25 GMT" "2013-04-26 GMT"
##  [117] "2013-04-27 GMT" "2013-04-28 GMT" "2013-04-29 GMT" "2013-04-30 GMT"
##  [121] "2013-05-01 GMT" "2013-05-02 GMT" "2013-05-03 GMT" "2013-05-04 GMT"
##  [125] "2013-05-05 GMT" "2013-05-06 GMT" "2013-05-07 GMT" "2013-05-08 GMT"
##  [129] "2013-05-09 GMT" "2013-05-10 GMT" "2013-05-11 GMT" "2013-05-12 GMT"
##  [133] "2013-05-13 GMT" "2013-05-14 GMT" "2013-05-15 GMT" "2013-05-16 GMT"
##  [137] "2013-05-17 GMT" "2013-05-18 GMT" "2013-05-19 GMT" "2013-05-20 GMT"
##  [141] "2013-05-21 GMT" "2013-05-22 GMT" "2013-05-23 GMT" "2013-05-24 GMT"
##  [145] "2013-05-25 GMT" "2013-05-26 GMT" "2013-05-27 GMT" "2013-05-28 GMT"
##  [149] "2013-05-29 GMT" "2013-05-30 GMT" "2013-05-31 GMT" "2013-06-01 GMT"
##  [153] "2013-06-02 GMT" "2013-06-03 GMT" "2013-06-04 GMT" "2013-06-05 GMT"
##  [157] "2013-06-06 GMT" "2013-06-07 GMT" "2013-06-08 GMT" "2013-06-09 GMT"
##  [161] "2013-06-10 GMT" "2013-06-11 GMT" "2013-06-12 GMT" "2013-06-13 GMT"
##  [165] "2013-06-14 GMT" "2013-06-15 GMT" "2013-06-16 GMT" "2013-06-17 GMT"
##  [169] "2013-06-18 GMT" "2013-06-19 GMT" "2013-06-20 GMT" "2013-06-21 GMT"
##  [173] "2013-06-22 GMT" "2013-06-23 GMT" "2013-06-24 GMT" "2013-06-25 GMT"
##  [177] "2013-06-26 GMT" "2013-06-27 GMT" "2013-06-28 GMT" "2013-06-29 GMT"
##  [181] "2013-06-30 GMT" "2013-07-01 GMT" "2013-07-02 GMT" "2013-07-03 GMT"
##  [185] "2013-07-04 GMT" "2013-07-05 GMT" "2013-07-06 GMT" "2013-07-07 GMT"
##  [189] "2013-07-08 GMT" "2013-07-09 GMT" "2013-07-10 GMT" "2013-07-11 GMT"
##  [193] "2013-07-12 GMT" "2013-07-13 GMT" "2013-07-14 GMT" "2013-07-15 GMT"
##  [197] "2013-07-16 GMT" "2013-07-17 GMT" "2013-07-18 GMT" "2013-07-19 GMT"
##  [201] "2013-07-20 GMT" "2013-07-21 GMT" "2013-07-22 GMT" "2013-07-23 GMT"
##  [205] "2013-07-24 GMT" "2013-07-25 GMT" "2013-07-26 GMT" "2013-07-27 GMT"
##  [209] "2013-07-28 GMT" "2013-07-29 GMT" "2013-07-30 GMT" "2013-07-31 GMT"
##  [213] "2013-08-01 GMT" "2013-08-02 GMT" "2013-08-03 GMT" "2013-08-04 GMT"
##  [217] "2013-08-05 GMT" "2013-08-06 GMT" "2013-08-07 GMT" "2013-08-08 GMT"
##  [221] "2013-08-09 GMT" "2013-08-10 GMT" "2013-08-11 GMT" "2013-08-12 GMT"
##  [225] "2013-08-13 GMT" "2013-08-14 GMT" "2013-08-15 GMT" "2013-08-16 GMT"
##  [229] "2013-08-17 GMT" "2013-08-18 GMT" "2013-08-19 GMT" "2013-08-20 GMT"
##  [233] "2013-08-21 GMT" "2013-08-22 GMT" "2013-08-23 GMT" "2013-08-24 GMT"
##  [237] "2013-08-25 GMT" "2013-08-26 GMT" "2013-08-27 GMT" "2013-08-28 GMT"
##  [241] "2013-08-29 GMT" "2013-08-30 GMT" "2013-08-31 GMT" "2013-09-01 GMT"
##  [245] "2013-09-02 GMT" "2013-09-03 GMT" "2013-09-04 GMT" "2013-09-05 GMT"
##  [249] "2013-09-06 GMT" "2013-09-07 GMT" "2013-09-08 GMT" "2013-09-09 GMT"
##  [253] "2013-09-10 GMT" "2013-09-11 GMT" "2013-09-12 GMT" "2013-09-13 GMT"
##  [257] "2013-09-14 GMT" "2013-09-15 GMT" "2013-09-16 GMT" "2013-09-17 GMT"
##  [261] "2013-09-18 GMT" "2013-09-19 GMT" "2013-09-20 GMT" "2013-09-21 GMT"
##  [265] "2013-09-22 GMT" "2013-09-23 GMT" "2013-09-24 GMT" "2013-09-25 GMT"
##  [269] "2013-09-26 GMT" "2013-09-27 GMT" "2013-09-28 GMT" "2013-09-29 GMT"
##  [273] "2013-09-30 GMT" "2013-10-01 GMT" "2013-10-02 GMT" "2013-10-03 GMT"
##  [277] "2013-10-04 GMT" "2013-10-05 GMT" "2013-10-06 GMT" "2013-10-07 GMT"
##  [281] "2013-10-08 GMT" "2013-10-09 GMT" "2013-10-10 GMT" "2013-10-11 GMT"
##  [285] "2013-10-12 GMT" "2013-10-13 GMT" "2013-10-14 GMT" "2013-10-15 GMT"
##  [289] "2013-10-16 GMT" "2013-10-17 GMT" "2013-10-18 GMT" "2013-10-19 GMT"
##  [293] "2013-10-20 GMT" "2013-10-21 GMT" "2013-10-22 GMT" "2013-10-23 GMT"
##  [297] "2013-10-24 GMT" "2013-10-25 GMT" "2013-10-26 GMT" "2013-10-27 GMT"
##  [301] "2013-10-28 GMT" "2013-10-29 GMT" "2013-10-30 GMT" "2013-10-31 GMT"
##  [305] "2013-11-01 GMT" "2013-11-02 GMT" "2013-11-03 GMT" "2013-11-04 GMT"
##  [309] "2013-11-05 GMT" "2013-11-06 GMT" "2013-11-07 GMT" "2013-11-08 GMT"
##  [313] "2013-11-09 GMT" "2013-11-10 GMT" "2013-11-11 GMT" "2013-11-12 GMT"
##  [317] "2013-11-13 GMT" "2013-11-14 GMT" "2013-11-15 GMT" "2013-11-16 GMT"
##  [321] "2013-11-17 GMT" "2013-11-18 GMT" "2013-11-19 GMT" "2013-11-20 GMT"
##  [325] "2013-11-21 GMT" "2013-11-22 GMT" "2013-11-23 GMT" "2013-11-24 GMT"
##  [329] "2013-11-25 GMT" "2013-11-26 GMT" "2013-11-27 GMT" "2013-11-28 GMT"
##  [333] "2013-11-29 GMT" "2013-11-30 GMT" "2013-12-01 GMT" "2013-12-02 GMT"
##  [337] "2013-12-03 GMT" "2013-12-04 GMT" "2013-12-05 GMT" "2013-12-06 GMT"
##  [341] "2013-12-07 GMT" "2013-12-08 GMT" "2013-12-09 GMT" "2013-12-10 GMT"
##  [345] "2013-12-11 GMT" "2013-12-12 GMT" "2013-12-13 GMT" "2013-12-14 GMT"
##  [349] "2013-12-15 GMT" "2013-12-16 GMT" "2013-12-17 GMT" "2013-12-18 GMT"
##  [353] "2013-12-19 GMT" "2013-12-20 GMT" "2013-12-21 GMT" "2013-12-22 GMT"
##  [357] "2013-12-23 GMT" "2013-12-24 GMT" "2013-12-25 GMT" "2013-12-26 GMT"
##  [361] "2013-12-27 GMT" "2013-12-28 GMT" "2013-12-29 GMT" "2013-12-30 GMT"
##  [365] "2013-12-31 GMT" "2014-01-01 GMT" "2014-01-02 GMT" "2014-01-03 GMT"
##  [369] "2014-01-04 GMT" "2014-01-05 GMT" "2014-01-06 GMT" "2014-01-07 GMT"
##  [373] "2014-01-08 GMT" "2014-01-09 GMT" "2014-01-10 GMT" "2014-01-11 GMT"
##  [377] "2014-01-12 GMT" "2014-01-13 GMT" "2014-01-14 GMT" "2014-01-15 GMT"
##  [381] "2014-01-16 GMT" "2014-01-17 GMT" "2014-01-18 GMT" "2014-01-19 GMT"
##  [385] "2014-01-20 GMT" "2014-01-21 GMT" "2014-01-22 GMT" "2014-01-23 GMT"
##  [389] "2014-01-24 GMT" "2014-01-25 GMT" "2014-01-26 GMT" "2014-01-27 GMT"
##  [393] "2014-01-28 GMT" "2014-01-29 GMT" "2014-01-30 GMT" "2014-01-31 GMT"
##  [397] "2014-02-01 GMT" "2014-02-02 GMT" "2014-02-03 GMT" "2014-02-04 GMT"
##  [401] "2014-02-05 GMT" "2014-02-06 GMT" "2014-02-07 GMT" "2014-02-08 GMT"
##  [405] "2014-02-09 GMT" "2014-02-10 GMT" "2014-02-11 GMT" "2014-02-12 GMT"
##  [409] "2014-02-13 GMT" "2014-02-14 GMT" "2014-02-15 GMT" "2014-02-16 GMT"
##  [413] "2014-02-17 GMT" "2014-02-18 GMT" "2014-02-19 GMT" "2014-02-20 GMT"
##  [417] "2014-02-21 GMT" "2014-02-22 GMT" "2014-02-23 GMT" "2014-02-24 GMT"
##  [421] "2014-02-25 GMT" "2014-02-26 GMT" "2014-02-27 GMT" "2014-02-28 GMT"
##  [425] "2014-03-01 GMT" "2014-03-02 GMT" "2014-03-03 GMT" "2014-03-04 GMT"
##  [429] "2014-03-05 GMT" "2014-03-06 GMT" "2014-03-07 GMT" "2014-03-08 GMT"
##  [433] "2014-03-09 GMT" "2014-03-10 GMT" "2014-03-11 GMT" "2014-03-12 GMT"
##  [437] "2014-03-13 GMT" "2014-03-14 GMT" "2014-03-15 GMT" "2014-03-16 GMT"
##  [441] "2014-03-17 GMT" "2014-03-18 GMT" "2014-03-19 GMT" "2014-03-20 GMT"
##  [445] "2014-03-21 GMT" "2014-03-22 GMT" "2014-03-23 GMT" "2014-03-24 GMT"
##  [449] "2014-03-25 GMT" "2014-03-26 GMT" "2014-03-27 GMT" "2014-03-28 GMT"
##  [453] "2014-03-29 GMT" "2014-03-30 GMT" "2014-03-31 GMT" "2014-04-01 GMT"
##  [457] "2014-04-02 GMT" "2014-04-03 GMT" "2014-04-04 GMT" "2014-04-05 GMT"
##  [461] "2014-04-06 GMT" "2014-04-07 GMT" "2014-04-08 GMT" "2014-04-09 GMT"
##  [465] "2014-04-10 GMT" "2014-04-11 GMT" "2014-04-12 GMT" "2014-04-13 GMT"
##  [469] "2014-04-14 GMT" "2014-04-15 GMT" "2014-04-16 GMT" "2014-04-17 GMT"
##  [473] "2014-04-18 GMT" "2014-04-19 GMT" "2014-04-20 GMT" "2014-04-21 GMT"
##  [477] "2014-04-22 GMT" "2014-04-23 GMT" "2014-04-24 GMT" "2014-04-25 GMT"
##  [481] "2014-04-26 GMT" "2014-04-27 GMT" "2014-04-28 GMT" "2014-04-29 GMT"
##  [485] "2014-04-30 GMT" "2014-05-01 GMT" "2014-05-02 GMT" "2014-05-03 GMT"
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##  [729] "2014-12-30 GMT" "2014-12-31 GMT" "2015-01-01 GMT" "2015-01-02 GMT"
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##  [749] "2015-01-19 GMT" "2015-01-20 GMT" "2015-01-21 GMT" "2015-01-22 GMT"
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##  [797] "2015-03-08 GMT" "2015-03-09 GMT" "2015-03-10 GMT" "2015-03-11 GMT"
##  [801] "2015-03-12 GMT" "2015-03-13 GMT" "2015-03-14 GMT" "2015-03-15 GMT"
##  [805] "2015-03-16 GMT" "2015-03-17 GMT" "2015-03-18 GMT" "2015-03-19 GMT"
##  [809] "2015-03-20 GMT" "2015-03-21 GMT" "2015-03-22 GMT" "2015-03-23 GMT"
##  [813] "2015-03-24 GMT" "2015-03-25 GMT" "2015-03-26 GMT" "2015-03-27 GMT"
##  [817] "2015-03-28 GMT" "2015-03-29 GMT" "2015-03-30 GMT" "2015-03-31 GMT"
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##  [825] "2015-04-05 GMT" "2015-04-06 GMT" "2015-04-07 GMT" "2015-04-08 GMT"
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##  [845] "2015-04-25 GMT" "2015-04-26 GMT" "2015-04-27 GMT" "2015-04-28 GMT"
##  [849] "2015-04-29 GMT" "2015-04-30 GMT" "2015-05-01 GMT" "2015-05-02 GMT"
##  [853] "2015-05-03 GMT" "2015-05-04 GMT" "2015-05-05 GMT" "2015-05-06 GMT"
##  [857] "2015-05-07 GMT" "2015-05-08 GMT" "2015-05-09 GMT" "2015-05-10 GMT"
##  [861] "2015-05-11 GMT" "2015-05-12 GMT" "2015-05-13 GMT" "2015-05-14 GMT"
##  [865] "2015-05-15 GMT" "2015-05-16 GMT" "2015-05-17 GMT" "2015-05-18 GMT"
##  [869] "2015-05-19 GMT" "2015-05-20 GMT" "2015-05-21 GMT" "2015-05-22 GMT"
##  [873] "2015-05-23 GMT" "2015-05-24 GMT" "2015-05-25 GMT" "2015-05-26 GMT"
##  [877] "2015-05-27 GMT" "2015-05-28 GMT" "2015-05-29 GMT" "2015-05-30 GMT"
##  [881] "2015-05-31 GMT" "2015-06-01 GMT" "2015-06-02 GMT" "2015-06-03 GMT"
##  [885] "2015-06-04 GMT" "2015-06-05 GMT" "2015-06-06 GMT" "2015-06-07 GMT"
##  [889] "2015-06-08 GMT" "2015-06-09 GMT" "2015-06-10 GMT" "2015-06-11 GMT"
##  [893] "2015-06-12 GMT" "2015-06-13 GMT" "2015-06-14 GMT" "2015-06-15 GMT"
##  [897] "2015-06-16 GMT" "2015-06-17 GMT" "2015-06-18 GMT" "2015-06-19 GMT"
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##  [905] "2015-06-24 GMT" "2015-06-25 GMT" "2015-06-26 GMT" "2015-06-27 GMT"
##  [909] "2015-06-28 GMT" "2015-06-29 GMT" "2015-06-30 GMT" "2015-07-01 GMT"
##  [913] "2015-07-02 GMT" "2015-07-03 GMT" "2015-07-04 GMT" "2015-07-05 GMT"
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##  [921] "2015-07-10 GMT" "2015-07-11 GMT" "2015-07-12 GMT" "2015-07-13 GMT"
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##  [937] "2015-07-26 GMT" "2015-07-27 GMT" "2015-07-28 GMT" "2015-07-29 GMT"
##  [941] "2015-07-30 GMT" "2015-07-31 GMT" "2015-08-01 GMT" "2015-08-02 GMT"
##  [945] "2015-08-03 GMT" "2015-08-04 GMT" "2015-08-05 GMT" "2015-08-06 GMT"
##  [949] "2015-08-07 GMT" "2015-08-08 GMT" "2015-08-09 GMT" "2015-08-10 GMT"
##  [953] "2015-08-11 GMT" "2015-08-12 GMT" "2015-08-13 GMT" "2015-08-14 GMT"
##  [957] "2015-08-15 GMT" "2015-08-16 GMT" "2015-08-17 GMT" "2015-08-18 GMT"
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##  [965] "2015-08-23 GMT" "2015-08-24 GMT" "2015-08-25 GMT" "2015-08-26 GMT"
##  [969] "2015-08-27 GMT" "2015-08-28 GMT" "2015-08-29 GMT" "2015-08-30 GMT"
##  [973] "2015-08-31 GMT" "2015-09-01 GMT" "2015-09-02 GMT" "2015-09-03 GMT"
##  [977] "2015-09-04 GMT" "2015-09-05 GMT" "2015-09-06 GMT" "2015-09-07 GMT"
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##  [985] "2015-09-12 GMT" "2015-09-13 GMT" "2015-09-14 GMT" "2015-09-15 GMT"
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## [1317] "2016-08-09 GMT" "2016-08-10 GMT" "2016-08-11 GMT" "2016-08-12 GMT"
## [1321] "2016-08-13 GMT" "2016-08-14 GMT" "2016-08-15 GMT" "2016-08-16 GMT"
## [1325] "2016-08-17 GMT" "2016-08-18 GMT" "2016-08-19 GMT" "2016-08-20 GMT"
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## [1333] "2016-08-25 GMT" "2016-08-26 GMT" "2016-08-27 GMT" "2016-08-28 GMT"
## [1337] "2016-08-29 GMT" "2016-08-30 GMT" "2016-08-31 GMT" "2016-09-01 GMT"
## [1341] "2016-09-02 GMT" "2016-09-03 GMT" "2016-09-04 GMT" "2016-09-05 GMT"
## [1345] "2016-09-06 GMT" "2016-09-07 GMT" "2016-09-08 GMT" "2016-09-09 GMT"
## [1349] "2016-09-10 GMT" "2016-09-11 GMT" "2016-09-12 GMT" "2016-09-13 GMT"
## [1353] "2016-09-14 GMT" "2016-09-15 GMT" "2016-09-16 GMT" "2016-09-17 GMT"
## [1357] "2016-09-18 GMT" "2016-09-19 GMT" "2016-09-20 GMT" "2016-09-21 GMT"
## [1361] "2016-09-22 GMT" "2016-09-23 GMT" "2016-09-24 GMT" "2016-09-25 GMT"
## [1365] "2016-09-26 GMT" "2016-09-27 GMT" "2016-09-28 GMT" "2016-09-29 GMT"
## [1369] "2016-09-30 GMT" "2016-10-01 GMT" "2016-10-02 GMT" "2016-10-03 GMT"
## [1373] "2016-10-04 GMT" "2016-10-05 GMT" "2016-10-06 GMT" "2016-10-07 GMT"
## [1377] "2016-10-08 GMT" "2016-10-09 GMT" "2016-10-10 GMT" "2016-10-11 GMT"
## [1381] "2016-10-12 GMT" "2016-10-13 GMT" "2016-10-14 GMT" "2016-10-15 GMT"
## [1385] "2016-10-16 GMT" "2016-10-17 GMT" "2016-10-18 GMT" "2016-10-19 GMT"
## [1389] "2016-10-20 GMT" "2016-10-21 GMT" "2016-10-22 GMT" "2016-10-23 GMT"
## [1393] "2016-10-24 GMT" "2016-10-25 GMT" "2016-10-26 GMT" "2016-10-27 GMT"
## [1397] "2016-10-28 GMT" "2016-10-29 GMT" "2016-10-30 GMT" "2016-10-31 GMT"
## [1401] "2016-11-01 GMT" "2016-11-02 GMT" "2016-11-03 GMT" "2016-11-04 GMT"
## [1405] "2016-11-05 GMT" "2016-11-06 GMT" "2016-11-07 GMT" "2016-11-08 GMT"
## [1409] "2016-11-09 GMT" "2016-11-10 GMT" "2016-11-11 GMT" "2016-11-12 GMT"
## [1413] "2016-11-13 GMT" "2016-11-14 GMT" "2016-11-15 GMT" "2016-11-16 GMT"
## [1417] "2016-11-17 GMT" "2016-11-18 GMT" "2016-11-19 GMT" "2016-11-20 GMT"
## [1421] "2016-11-21 GMT" "2016-11-22 GMT" "2016-11-23 GMT" "2016-11-24 GMT"
## [1425] "2016-11-25 GMT" "2016-11-26 GMT" "2016-11-27 GMT" "2016-11-28 GMT"
## [1429] "2016-11-29 GMT" "2016-11-30 GMT" "2016-12-01 GMT" "2016-12-02 GMT"
## [1433] "2016-12-03 GMT" "2016-12-04 GMT" "2016-12-05 GMT" "2016-12-06 GMT"
## [1437] "2016-12-07 GMT" "2016-12-08 GMT" "2016-12-09 GMT" "2016-12-10 GMT"
## [1441] "2016-12-11 GMT" "2016-12-12 GMT" "2016-12-13 GMT" "2016-12-14 GMT"
## [1445] "2016-12-15 GMT" "2016-12-16 GMT" "2016-12-17 GMT" "2016-12-18 GMT"
## [1449] "2016-12-19 GMT" "2016-12-20 GMT" "2016-12-21 GMT" "2016-12-22 GMT"
## [1453] "2016-12-23 GMT" "2016-12-24 GMT" "2016-12-25 GMT" "2016-12-26 GMT"
## [1457] "2016-12-27 GMT" "2016-12-28 GMT" "2016-12-29 GMT" "2016-12-30 GMT"
## [1461] "2016-12-31 GMT"
## 
## $train.holiday.names
## NULL
## 
## $train.component.cols
##    additive_terms daily weekly yearly multiplicative_terms
## 1               1     0      0      1                    0
## 2               1     0      0      1                    0
## 3               1     0      0      1                    0
## 4               1     0      0      1                    0
## 5               1     0      0      1                    0
## 6               1     0      0      1                    0
## 7               1     0      0      1                    0
## 8               1     0      0      1                    0
## 9               1     0      0      1                    0
## 10              1     0      0      1                    0
## 11              1     0      0      1                    0
## 12              1     0      0      1                    0
## 13              1     0      0      1                    0
## 14              1     0      0      1                    0
## 15              1     0      0      1                    0
## 16              1     0      0      1                    0
## 17              1     0      0      1                    0
## 18              1     0      0      1                    0
## 19              1     0      0      1                    0
## 20              1     0      0      1                    0
## 21              1     0      1      0                    0
## 22              1     0      1      0                    0
## 23              1     0      1      0                    0
## 24              1     0      1      0                    0
## 25              1     0      1      0                    0
## 26              1     0      1      0                    0
## 27              1     1      0      0                    0
## 28              1     1      0      0                    0
## 29              1     1      0      0                    0
## 30              1     1      0      0                    0
## 31              1     1      0      0                    0
## 32              1     1      0      0                    0
## 33              1     1      0      0                    0
## 34              1     1      0      0                    0
## 
## $component.modes
## $component.modes$additive
## [1] "yearly"                    "weekly"                   
## [3] "daily"                     "additive_terms"           
## [5] "extra_regressors_additive" "holidays"                 
## 
## $component.modes$multiplicative
## [1] "multiplicative_terms"            "extra_regressors_multiplicative"
## 
## 
## $fit.kwargs
## list()
## 
## attr(,"class")
## [1] "prophet" "list"

Berdasarkan hasil fitting model diatas bisa dijelaslkan bahwa model_ts sekarang menyimpan informasi data permintaan harian pada store 03. Sehingga kita bisa gunakan untuk mengekstrak informasi deret waktu tersebut untuk melakukan perkiraan selama periode waktu yang bisa ditentukan. Misalnya kita akan memperkiraan permintaan penjualan untuk 1 tahun kedepan. Utuk melakukan ini kita harus menyiapkan data frame yang terdiri dari rentang waktu/tanggal mendatang yang akan diperkirakan. Untungnya dalam prophet() sudah menyediakan sebuah fungsi make_future_dataframe() memudahkan kita untuk menyiapkan data tersebut.

range(train_daily_3$ds)

## [1] "2013-01-01" "2016-12-31"

Bisa dilihat bahwa jangka waktu prediksi mulai dari 2013 s/d 2016

Menyiapkan tanggal untuk prediksi

Periode prediksi adalah 1 tahun kedepan atau 365 hari

# menyiapkan tanggal utk prediksi
future_ts <- make_future_dataframe(model_ts, periods = 365, freq = "day")
glimpse(future_ts)

## Rows: 1,826
## Columns: 1
## $ ds <dttm> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0…

Visualisasi hasil forecasting untuk perkiraan data 1 tahun kedepan

# visualisasi hasil forecasting
forecast_ts <- predict(model_ts, future_ts)
plot(model_ts, forecast_ts)

Bisa dilihat bahwa, gambar pada grafik yang berwarna biru menunjukkan hasil forecast yang sudah dilakukan. Titik hitam menunjukkan data dari mulai 2013 sampai 2016. Waktu biru yang tidak ada titik adalah perkiraan permintaan untuk 2017

Visualisasi komponen model

Dengan prophet dimungkinkan kita memvisulisasikan berdasarkan trend, weekly, dan yearly. Default: - daily: sampling hourly, dan frequency 24 - weekly: sampling daily, dan frequency 7 - yearly: sampling daily dan frequency 365

#visualiasi komponen model
prophet_plot_components(model_ts, forecast_ts)

Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:

• Penjualan dari tahun ke tahun meningkat, dimana penjualan di tahun 2017 adalah penjualan yang tertinggi
• Penjualan terbanyak pada setiap bulan dan tahun cendrung mengalami peningkatan di hari weekend, yaitu hari Jumat, Sabtu dan Minggu, sementara penjualan di hari Senin adalah penjualan terendah dibandingakan dengn hari yang lain
• Periode penjualan dalam setahun yang paling tinggi adalah pada bulan Juni, Juli dan Agustus, sedangkan tingkat penjualan terendah pada bulan Januari

forecast berdasarkan seasionality bulan

# forecast berdasarkan seasionality month (bulan)
model_ts_monthly <- prophet(changepoint.prior.scale = 0.05, 
                    yearly.seasonality = FALSE) %>% 
  add_seasonality(name = "monthly", period = 30.5, fourier.order = 3) %>% 
  fit.prophet(train_daily_3) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_ts_monthly <- make_future_dataframe(model_ts_monthly, periods = 365) 
forecast_ts_monthly <- predict(model_ts_monthly, future_ts_monthly) 
prophet_plot_components(model_ts_monthly, forecast_ts_monthly)

Visualisasi trend permintaan

Dalam kasus ini kita akan memvisualisasi tren permintaan dari awal tahun 2017 sampai akhir 2017

#visualisasi dari tren awal 2017 sampai akhir 2017
plot(model_ts_monthly, forecast_ts_monthly)

Bisa dilihat bahwa terjadi nya trend peningkatan permintaan yang relatif tinggi dibandingkan tahun sebelumnya

forecast berdasarkan seasionality penambahan holiday (hari libur)

# Menetapkan hari libur mulai dari tahun 2013 sampai 2016, misal libur di hari natal 25 desember atau tahun baru setiap tanggal 31 desember
holiday <- 
  data.frame( 
    holiday = "newyeareve", 
    ds = dmy(c("31-12-2013","31-12-2014", "31-12-2015", "31-12-2016", "31-12-2017")), 
    lower_window = -5, 
    upper_window = 0 
  ) 
holiday 

##      holiday         ds lower_window upper_window
## 1 newyeareve 2013-12-31           -5            0
## 2 newyeareve 2014-12-31           -5            0
## 3 newyeareve 2015-12-31           -5            0
## 4 newyeareve 2016-12-31           -5            0
## 5 newyeareve 2017-12-31           -5            0

# visualisasi hasil forecast dengan penambahan efek holiday
model_ts_holiday <- prophet(changepoint.prior.scale = 0.05, 
                    holidays = holiday) %>% 
  add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>% 
  fit.prophet(train_daily_3) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_ts_holiday <- make_future_dataframe(model_ts_holiday, periods = 365) 
forecast_ts_holiday <- predict(model_ts_holiday, future_ts_holiday) 
plot(model_ts_holiday, forecast_ts_holiday)

# melihat trend dan holiday effect dari perkiraan
prophet_plot_components(model_ts_holiday, forecast_ts_holiday)

Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:

1. Berdasarkan penjualan mingguan didapatkan bahwa penjualan meningkat diawal bulan
2. Dengan menambahkan seasionality holiday didapatkan bahwa trend peningkatan penjualan berada pada akhir tahun yaitu dibulan desember-januari

Melihat hasil perkiraan berdasarkan trend dan seasonality

forecast_ts %>%
  select(ds, trend, weekly, yearly, yhat)

##              ds    trend     weekly       yearly     yhat
## 1    2013-01-01 1777.267 -218.55228 -843.8701017 1480.175
## 2    2013-01-02 1776.102 -213.16223 -846.1356825 1482.134
## 3    2013-01-03 1774.937  -29.41662 -849.0561370 1661.794
## 4    2013-01-04 1773.772  159.07673 -852.5068489 1845.672
## 5    2013-01-05 1772.607  356.13985 -856.3437163 2037.733
## 6    2013-01-06 1771.442  545.36929 -860.4087772 2221.732
## 7    2013-01-07 1770.277 -599.45476 -864.5359552 1071.616
## 8    2013-01-08 1769.112 -218.55228 -868.5567610 1447.333
## 9    2013-01-09 1767.947 -213.16223 -872.3057870 1447.809
## 10   2013-01-10 1766.782  -29.41662 -875.6258449 1627.069
## 11   2013-01-11 1765.617  159.07673 -878.3726131 1811.651
## 12   2013-01-12 1764.452  356.13985 -880.4186749 2005.503
## 13   2013-01-13 1763.287  545.36929 -881.6568526 2192.329
## 14   2013-01-14 1762.122 -599.45476 -882.0027655 1045.994
## 15   2013-01-15 1760.957 -218.55228 -881.3965617 1426.338
## 16   2013-01-16 1759.792 -213.16223 -879.8038049 1432.156
## 17   2013-01-17 1758.627  -29.41662 -877.2155158 1617.324
## 18   2013-01-18 1757.462  159.07673 -873.6473981 1808.221
## 19   2013-01-19 1756.297  356.13985 -869.1382997 2008.628
## 20   2013-01-20 1755.132  545.36929 -863.7479820 2202.083
## 21   2013-01-21 1753.967 -599.45476 -857.5542877 1062.287
## 22   2013-01-22 1752.802 -218.55228 -850.6498156 1448.929
## 23   2013-01-23 1751.637 -213.16223 -843.1382197 1460.666
## 24   2013-01-24 1750.471  -29.41662 -835.1302606 1651.254
## 25   2013-01-25 1749.306  159.07673 -826.7397413 1846.973
## 26   2013-01-26 1748.141  356.13985 -818.0794581 2051.532
## 27   2013-01-27 1746.976  545.36929 -809.2572965 2248.418
## 28   2013-01-28 1745.811 -599.45476 -800.3725923 1111.314
## 29   2013-01-29 1744.646 -218.55228 -791.5128679 1499.911
## 30   2013-01-30 1743.481 -213.16223 -782.7510414 1512.898
## 31   2013-01-31 1742.316  -29.41662 -774.1431871 1704.086
## 32   2013-02-01 1741.151  159.07673 -765.7269097 1899.831
## 33   2013-02-02 1739.986  356.13985 -757.5203723 2103.935
## 34   2013-02-03 1738.821  545.36929 -749.5219996 2299.998
## 35   2013-02-04 1737.656 -599.45476 -741.7108539 1161.820
## 36   2013-02-05 1736.491 -218.55228 -734.0476629 1549.221
## 37   2013-02-06 1735.326 -213.16223 -726.4764565 1561.017
## 38   2013-02-07 1734.161  -29.41662 -718.9267535 1751.147
## 39   2013-02-08 1732.996  159.07673 -711.3162207 1946.086
## 40   2013-02-09 1731.831  356.13985 -703.5537147 2149.747
## 41   2013-02-10 1730.666  545.36929 -695.5426063 2345.822
## 42   2013-02-11 1729.501 -599.45476 -687.1842773 1208.192
## 43   2013-02-12 1728.336 -218.55228 -678.3816795 1596.732
## 44   2013-02-13 1727.171 -213.16223 -669.0428402 1610.296
## 45   2013-02-14 1726.006  -29.41662 -659.0842057 1802.835
## 46   2013-02-15 1724.841  159.07673 -648.4337167 2000.814
## 47   2013-02-16 1723.676  356.13985 -637.0335213 2208.112
## 48   2013-02-17 1722.511  545.36929 -624.8422410 2408.368
## 49   2013-02-18 1721.346 -599.45476 -611.8367224 1275.384
## 50   2013-02-19 1720.181 -218.55228 -598.0132186 1668.945
## 51   2013-02-20 1719.016 -213.16223 -583.3879687 1687.795
## 52   2013-02-21 1717.850  -29.41662 -567.9971554 1885.767
## 53   2013-02-22 1716.685  159.07673 -551.8962456 2089.196
## 54   2013-02-23 1715.520  356.13985 -535.1587331 2301.831
## 55   2013-02-24 1714.355  545.36929 -517.8743232 2507.180
## 56   2013-02-25 1713.190 -599.45476 -500.1466145 1378.919
## 57   2013-02-26 1712.025 -218.55228 -482.0903481 1776.713
## 58   2013-02-27 1710.860 -213.16223 -463.8283069 1799.200
## 59   2013-02-28 1709.695  -29.41662 -445.4879589 2000.121
## 60   2013-03-01 1708.530  159.07673 -427.1979430 2205.739
## 61   2013-03-02 1707.365  356.13985 -409.0845034 2419.750
## 62   2013-03-03 1706.200  545.36929 -391.2679775 2625.631
## 63   2013-03-04 1705.035 -599.45476 -373.8594398 1497.051
## 64   2013-03-05 1703.870 -218.55228 -356.9576028 1893.690
## 65   2013-03-06 1702.705 -213.16223 -340.6460618 1914.227
## 66   2013-03-07 1701.540  -29.41662 -324.9909677 2112.462
## 67   2013-03-08 1700.375  159.07673 -310.0391919 2314.742
## 68   2013-03-09 1699.210  356.13985 -295.8170377 2524.863
## 69   2013-03-10 1698.045  545.36929 -282.3295346 2726.414
## 70   2013-03-11 1696.880 -599.45476 -269.5603347 1593.195
## 71   2013-03-12 1695.715 -218.55228 -257.4722138 1985.020
## 72   2013-03-13 1694.550 -213.16223 -246.0081622 2000.709
## 73   2013-03-14 1693.385  -29.41662 -235.0930331 2194.205
## 74   2013-03-15 1692.220  159.07673 -224.6357000 2391.991
## 75   2013-03-16 1691.055  356.13985 -214.5316633 2597.993
## 76   2013-03-17 1689.890  545.36929 -204.6660291 2795.923
## 77   2013-03-18 1688.725 -599.45476 -194.9167779 1659.683
## 78   2013-03-19 1687.560 -218.55228 -185.1582296 2049.179
## 79   2013-03-20 1686.395 -213.16223 -175.2646091 2063.298
## 80   2013-03-21 1685.229  -29.41662 -165.1136120 2256.029
## 81   2013-03-22 1684.064  159.07673 -154.5898721 2453.881
## 82   2013-03-23 1682.899  356.13985 -143.5882372 2660.781
## 83   2013-03-24 1681.734  545.36929 -132.0167615 2860.417
## 84   2013-03-25 1680.569 -599.45476 -119.7993373 1726.645
## 85   2013-03-26 1679.404 -218.55228 -106.8778937 2119.304
## 86   2013-03-27 1678.239 -213.16223  -93.2141072 2137.193
## 87   2013-03-28 1677.074  -29.41662  -78.7905803 2334.197
## 88   2013-03-29 1675.909  159.07673  -63.6114599 2536.704
## 89   2013-03-30 1674.744  356.13985  -47.7024841 2748.511
## 90   2013-03-31 1673.579  545.36929  -31.1104604 2953.168
## 91   2013-04-01 1672.414 -599.45476  -13.9021937 1824.387
## 92   2013-04-02 1671.249 -218.55228    3.8371007 2221.864
## 93   2013-04-03 1670.084 -213.16223   22.0058532 2244.258
## 94   2013-04-04 1668.919  -29.41662   40.4886046 2445.321
## 95   2013-04-05 1667.754  159.07673   59.1588111 2651.319
## 96   2013-04-06 1666.589  356.13985   77.8819095 2865.941
## 97   2013-04-07 1665.424  545.36929   96.5185621 3072.642
## 98   2013-04-08 1664.259 -599.45476  114.9279911 1945.062
## 99   2013-04-09 1663.094 -218.55228  132.9713162 2342.843
## 100  2013-04-10 1661.929 -213.16223  150.5148089 2364.611
## 101  2013-04-11 1660.764  -29.41662  167.4329796 2564.110
## 102  2013-04-12 1659.599  159.07673  183.6114214 2767.617
## 103  2013-04-13 1658.434  356.13985  198.9493422 2978.853
## 104  2013-04-14 1657.269  545.36929  213.3617255 3181.330
## 105  2013-04-15 1656.104 -599.45476  226.7810725 2048.760
## 106  2013-04-16 1654.939 -218.55228  239.1586893 2440.875
## 107  2013-04-17 1653.774 -213.16223  250.4654973 2456.407
## 108  2013-04-18 1652.608  -29.41662  260.6923567 2649.214
## 109  2013-04-19 1651.443  159.07673  269.8499068 2845.700
## 110  2013-04-20 1650.278  356.13985  277.9679392 3049.716
## 111  2013-04-21 1649.113  545.36929  285.0943328 3244.907
## 112  2013-04-22 1647.948 -599.45476  291.2935882 2105.117
## 113  2013-04-23 1646.783 -218.55228  296.6450118 2490.206
## 114  2013-04-24 1645.618 -213.16223  301.2406031 2499.027
## 115  2013-04-25 1644.453  -29.41662  305.1827104 2685.549
## 116  2013-04-26 1643.288  159.07673  308.5815181 2876.276
## 117  2013-04-27 1642.123  356.13985  311.5524359 3075.145
## 118  2013-04-28 1640.958  545.36929  314.2134574 3265.871
## 119  2013-04-29 1639.793 -599.45476  316.6825557 2122.351
## 120  2013-04-30 1638.628 -218.55228  319.0751773 2504.481
## 121  2013-05-01 1637.463 -213.16223  321.5018946 2511.133
## 122  2013-05-02 1636.298  -29.41662  324.0662671 2696.278
## 123  2013-05-03 1635.133  159.07673  326.8629546 2886.403
## 124  2013-05-04 1633.968  356.13985  329.9761189 3085.414
## 125  2013-05-05 1632.803  545.36929  333.4781384 3276.980
## 126  2013-05-06 1631.638 -599.45476  337.4286525 2134.942
## 127  2013-05-07 1630.473 -218.55228  341.8739430 2519.124
## 128  2013-05-08 1629.308 -213.16223  346.8466484 2528.322
## 129  2013-05-09 1628.143  -29.41662  352.3658022 2716.422
## 130  2013-05-10 1626.978  159.07673  358.4371732 2909.821
## 131  2013-05-11 1625.813  356.13985  365.0538842 3112.336
## 132  2013-05-12 1624.648  545.36929  372.1972753 3307.544
## 133  2013-05-13 1623.483 -599.45476  379.8379765 2169.196
## 134  2013-05-14 1622.318 -218.55228  387.9371491 2557.032
## 135  2013-05-15 1621.153 -213.16223  396.4478554 2569.768
## 136  2013-05-16 1619.988  -29.41662  405.3165146 2761.217
## 137  2013-05-17 1618.822  159.07673  414.4844027 2957.713
## 138  2013-05-18 1617.657  356.13985  423.8891606 3163.016
## 139  2013-05-19 1616.492  545.36929  433.4662716 3360.658
## 140  2013-05-20 1615.327 -599.45476  443.1504782 2224.353
## 141  2013-05-21 1614.162 -218.55228  452.8771121 2613.817
## 142  2013-05-22 1613.919 -213.16223  462.5833129 2628.670
## 143  2013-05-23 1613.675  -29.41662  472.2091228 2821.798
## 144  2013-05-24 1613.432  159.07673  481.6984435 3019.537
## 145  2013-05-25 1613.188  356.13985  490.9998513 3225.658
## 146  2013-05-26 1612.945  545.36929  500.0672693 3423.711
## 147  2013-05-27 1612.701 -599.45476  508.8605013 2287.437
## 148  2013-05-28 1612.458 -218.55228  517.3456332 2676.581
## 149  2013-05-29 1612.214 -213.16223  525.4953146 2689.877
## 150  2013-05-30 1611.971  -29.41662  533.2889310 2881.173
## 151  2013-05-31 1611.727  159.07673  540.7126815 3076.846
## 152  2013-06-01 1611.484  356.13985  547.7595760 3280.713
## 153  2013-06-02 1611.240  545.36929  554.4293639 3476.369
## 154  2013-06-03 1610.997 -599.45476  560.7284079 2337.600
## 155  2013-06-04 1610.753 -218.55228  566.6695112 2724.200
## 156  2013-06-05 1610.509 -213.16223  572.2717071 2734.949
## 157  2013-06-06 1610.266  -29.41662  577.5600137 2923.739
## 158  2013-06-07 1610.022  159.07673  582.5651565 3116.994
## 159  2013-06-08 1609.779  356.13985  587.3232565 3318.572
## 160  2013-06-09 1609.535  545.36929  591.8754788 3512.110
## 161  2013-06-10 1609.292 -599.45476  596.2676358 2371.435
## 162  2013-06-11 1609.048 -218.55228  600.5497344 2756.376
## 163  2013-06-12 1608.805 -213.16223  604.7754578 2765.748
## 164  2013-06-13 1608.561  -29.41662  609.0015708 2953.476
## 165  2013-06-14 1608.318  159.07673  613.2872366 3146.012
## 166  2013-06-15 1608.074  356.13985  617.6932390 3347.237
## 167  2013-06-16 1607.831  545.36929  622.2810983 3540.811
## 168  2013-06-17 1607.587 -599.45476  627.1120812 2400.574
## 169  2013-06-18 1607.344 -218.55228  632.2461015 2786.367
## 170  2013-06-19 1607.100 -213.16223  637.7405172 2797.008
## 171  2013-06-20 1606.857  -29.41662  643.6488331 2986.419
## 172  2013-06-21 1606.613  159.07673  650.0193237 3181.039
## 173  2013-06-22 1606.370  356.13985  656.8935978 3384.733
## 174  2013-06-23 1606.126  545.36929  664.3051292 3581.130
## 175  2013-06-24 1605.882 -599.45476  672.2777861 2444.035
## 176  2013-06-25 1605.639 -218.55228  680.8243947 2833.241
## 177  2013-06-26 1605.395 -213.16223  689.9453766 2847.508
## 178  2013-06-27 1605.152  -29.41662  699.6275032 3040.693
## 179  2013-06-28 1604.908  159.07673  709.8428108 3239.158
## 180  2013-06-29 1604.665  356.13985  720.5477218 3446.682
## 181  2013-06-30 1604.421  545.36929  731.6824152 3646.803
## 182  2013-07-01 1604.178 -599.45476  743.1704878 2513.223
## 183  2013-07-02 1603.934 -218.55228  754.9189422 2905.631
## 184  2013-07-03 1603.691 -213.16223  766.8185341 2922.677
## 185  2013-07-04 1603.447  -29.41662  778.7445007 3118.105
## 186  2013-07-05 1603.204  159.07673  790.5576876 3318.168
## 187  2013-07-06 1602.960  356.13985  802.1060783 3526.536
## 188  2013-07-07 1602.717  545.36929  813.2267228 3726.643
## 189  2013-07-08 1604.118 -599.45476  823.7480485 2593.741
## 190  2013-07-09 1605.520 -218.55228  833.4925259 2985.790
## 191  2013-07-10 1606.921 -213.16223  842.2796515 3001.368
## 192  2013-07-11 1608.323  -29.41662  849.9291960 3194.165
## 193  2013-07-12 1609.724  159.07673  856.2646596 3390.395
## 194  2013-07-13 1611.126  356.13985  861.1168634 3593.712
## 195  2013-07-14 1612.527  545.36929  864.3276006 3787.554
## 196  2013-07-15 1613.929 -599.45476  865.7532632 2645.557
## 197  2013-07-16 1615.330 -218.55228  865.2683579 3027.376
## 198  2013-07-17 1616.732 -213.16223  862.7688204 3031.668
## 199  2013-07-18 1618.133  -29.41662  858.1750400 3212.221
## 200  2013-07-19 1619.534  159.07673  851.4345087 3395.376
## 201  2013-07-20 1620.936  356.13985  842.5240123 3584.930
## 202  2013-07-21 1622.337  545.36929  831.4512933 3764.488
## 203  2013-07-22 1623.739 -599.45476  818.2561207 2607.870
## 204  2013-07-23 1625.140 -218.55228  803.0107173 2974.929
## 205  2013-07-24 1626.542 -213.16223  785.8195079 2964.529
## 206  2013-07-25 1627.943  -29.41662  766.8181677 3130.675
## 207  2013-07-26 1629.345  159.07673  746.1719679 3299.923
## 208  2013-07-27 1630.746  356.13985  724.0734309 3476.289
## 209  2013-07-28 1632.148  545.36929  700.7393282 3643.586
## 210  2013-07-29 1633.549 -599.45476  676.4070697 2475.831
## 211  2013-07-30 1634.951 -218.55228  651.3305503 2833.059
## 212  2013-07-31 1636.352 -213.16223  625.7755367 2814.295
## 213  2013-08-01 1637.754  -29.41662  600.0146899 2973.682
## 214  2013-08-02 1639.155  159.07673  574.3223318 3137.884
## 215  2013-08-03 1640.557  356.13985  548.9690725 3310.996
## 216  2013-08-04 1641.958  545.36929  524.2164240 3476.874
## 217  2013-08-05 1643.360 -599.45476  500.3115270 2309.546
## 218  2013-08-06 1644.761 -218.55228  477.4821187 2669.021
## 219  2013-08-07 1646.163 -213.16223  455.9318676 2654.262
## 220  2013-08-08 1647.564  -29.41662  435.8361925 2819.314
## 221  2013-08-09 1648.966  159.07673  417.3386752 2990.711
## 222  2013-08-10 1650.367  356.13985  400.5481633 3172.385
## 223  2013-08-11 1651.769  545.36929  385.5366421 3348.004
## 224  2013-08-12 1653.170 -599.45476  372.3379391 2191.383
## 225  2013-08-13 1654.572 -218.55228  360.9473034 2562.296
## 226  2013-08-14 1655.973 -213.16223  351.3218793 2559.463
## 227  2013-08-15 1657.375  -29.41662  343.3820730 2736.670
## 228  2013-08-16 1658.776  159.07673  337.0137879 2920.196
## 229  2013-08-17 1660.178  356.13985  332.0714798 3113.719
## 230  2013-08-18 1661.579  545.36929  328.3819633 3300.660
## 231  2013-08-19 1662.981 -599.45476  325.7488793 2154.604
## 232  2013-08-20 1664.382 -218.55228  323.9577162 2535.117
## 233  2013-08-21 1665.783 -213.16223  322.7812601 2540.732
## 234  2013-08-22 1667.185  -29.41662  321.9853385 2725.084
## 235  2013-08-23 1669.274  159.07673  321.3347113 2915.015
## 236  2013-08-24 1671.362  356.13985  320.5989596 3113.431
## 237  2013-08-25 1673.451  545.36929  319.5582181 3303.708
## 238  2013-08-26 1675.540 -599.45476  318.0086034 2159.423
## 239  2013-08-27 1677.628 -218.55228  315.7671938 2540.173
## 240  2013-08-28 1679.717 -213.16223  312.6764304 2544.561
## 241  2013-08-29 1681.806  -29.41662  308.6078192 2726.327
## 242  2013-08-30 1683.894  159.07673  303.4648366 2911.766
## 243  2013-08-31 1685.983  356.13985  297.1849578 3104.638
## 244  2013-09-01 1688.071  545.36929  289.7407524 3288.511
## 245  2013-09-02 1690.160 -599.45476  281.1400156 2137.175
## 246  2013-09-03 1692.249 -218.55228  271.4249298 2510.451
## 247  2013-09-04 1694.337 -213.16223  260.6702789 2507.175
## 248  2013-09-05 1696.426  -29.41662  248.9807609 2681.320
## 249  2013-09-06 1698.515  159.07673  236.4874738 2859.409
## 250  2013-09-07 1700.603  356.13985  223.3436686 3045.417
## 251  2013-09-08 1702.692  545.36929  209.7198888 3223.111
## 252  2013-09-09 1704.781 -599.45476  195.7986300 2066.454
## 253  2013-09-10 1706.869 -218.55228  181.7686703 2435.416
## 254  2013-09-11 1708.958 -213.16223  167.8192322 2428.945
## 255  2013-09-12 1711.047  -29.41662  154.1341415 2601.094
## 256  2013-09-13 1713.135  159.07673  140.8861523 2778.428
## 257  2013-09-14 1715.224  356.13985  128.2316030 2964.925
## 258  2013-09-15 1717.313  545.36929  116.3055604 3144.317
## 259  2013-09-16 1719.401 -599.45476  105.2175979 1990.494
## 260  2013-09-17 1721.490 -218.55228   95.0483363 2363.316
## 261  2013-09-18 1723.579 -213.16223   85.8468555 2361.593
## 262  2013-09-19 1725.667  -29.41662   77.6290634 2539.210
## 263  2013-09-20 1727.756  159.07673   70.3770796 2722.540
## 264  2013-09-21 1729.845  356.13985   64.0396660 2915.354
## 265  2013-09-22 1731.933  545.36929   58.5337048 3101.166
## 266  2013-09-23 1734.022 -599.45476   53.7466955 1953.644
## 267  2013-09-24 1736.111 -218.55228   49.5402136 2332.428
## 268  2013-09-25 1738.199 -213.16223   45.7542432 2336.121
## 269  2013-09-26 1740.288  -29.41662   42.2122725 2518.413
## 270  2013-09-27 1742.376  159.07673   38.7270145 2705.510
## 271  2013-09-28 1744.465  356.13985   35.1065980 2901.041
## 272  2013-09-29 1746.554  545.36929   31.1610554 3088.414
## 273  2013-09-30 1748.642 -599.45476   26.7089238 1941.226
## 274  2013-10-01 1750.731 -218.55228   21.5837696 2319.092
## 275  2013-10-02 1752.820 -213.16223   15.6404434 2320.628
## 276  2013-10-03 1754.908  -29.41662    8.7608790 2499.583
## 277  2013-10-04 1756.997  159.07673    0.8592559 2682.263
## 278  2013-10-05 1759.086  356.13985   -8.1136378 2872.442
## 279  2013-10-06 1761.174  545.36929  -18.1669883 3053.707
## 280  2013-10-07 1763.263 -599.45476  -29.2676077 1899.871
## 281  2013-10-08 1765.352 -218.55228  -41.3387481 2270.790
## 282  2013-10-09 1767.440 -213.16223  -54.2601449 2265.348
## 283  2013-10-10 1769.529  -29.41662  -67.8693208 2437.573
## 284  2013-10-11 1771.618  159.07673  -81.9641511 2614.060
## 285  2013-10-12 1773.706  356.13985  -96.3066533 2798.869
## 286  2013-10-13 1775.795  545.36929 -110.6279327 2975.866
## 287  2013-10-14 1777.884 -599.45476 -124.6341826 1819.125
## 288  2013-10-15 1779.972 -218.55228 -138.0136052 2188.736
## 289  2013-10-16 1782.061 -213.16223 -150.4440953 2183.784
## 290  2013-10-17 1784.150  -29.41662 -161.6015022 2358.461
## 291  2013-10-18 1786.238  159.07673 -171.1682680 2539.477
## 292  2013-10-19 1788.327  356.13985 -178.8422250 2730.954
## 293  2013-10-20 1790.416  545.36929 -184.3453285 2916.769
## 294  2013-10-21 1792.504 -599.45476 -187.4320959 1770.947
## 295  2013-10-22 1794.593 -218.55228 -187.8975279 2153.473
## 296  2013-10-23 1796.681 -213.16223 -185.5842965 2163.265
## 297  2013-10-24 1798.770  -29.41662 -180.3889986 2354.294
## 298  2013-10-25 1800.859  159.07673 -172.2672942 2552.998
## 299  2013-10-26 1802.947  356.13985 -161.2377753 2763.179
## 300  2013-10-27 1805.036  545.36929 -147.3844381 2968.351
## 301  2013-10-28 1807.125 -599.45476 -130.8576659 1842.142
## 302  2013-10-29 1809.213 -218.55228 -111.8736672 2244.117
## 303  2013-10-30 1811.302 -213.16223  -90.7123481 2272.757
## 304  2013-10-31 1813.391  -29.41662  -67.7136403 2481.590
## 305  2013-11-01 1815.479  159.07673  -43.2723417 2696.614
## 306  2013-11-02 1817.568  356.13985  -17.8315668 2921.206
## 307  2013-11-03 1819.657  545.36929    8.1250629 3138.481
## 308  2013-11-04 1821.745 -599.45476   34.0823238 2021.703
## 309  2013-11-05 1823.834 -218.55228   59.5031979 2430.115
## 310  2013-11-06 1825.923 -213.16223   83.8393661 2461.930
## 311  2013-11-07 1828.011  -29.41662  106.5421522 2670.467
## 312  2013-11-08 1830.100  159.07673  127.0736677 2881.580
## 313  2013-11-09 1832.189  356.13985  144.9179027 3098.576
## 314  2013-11-10 1834.277  545.36929  159.5915046 3304.568
## 315  2013-11-11 1836.366 -599.45476  170.6539952 2172.895
## 316  2013-11-12 1838.455 -218.55228  177.7171863 2562.949
## 317  2013-11-13 1840.543 -213.16223  180.4535726 2573.164
## 318  2013-11-14 1842.632  -29.41662  178.6035043 2757.149
## 319  2013-11-15 1844.720  159.07673  171.9809685 2941.108
## 320  2013-11-16 1846.809  356.13985  160.4778450 3128.757
## 321  2013-11-17 1848.898  545.36929  144.0665325 3303.663
## 322  2013-11-18 1850.986 -599.45476  122.8008841 2139.662
## 323  2013-11-19 1853.075 -218.55228   96.8154296 2496.668
## 324  2013-11-20 1855.164 -213.16223   66.3229012 2473.654
## 325  2013-11-21 1857.252  -29.41662   31.6101225 2624.776
## 326  2013-11-22 1859.341  159.07673   -6.9676448 2776.780
## 327  2013-11-23 1861.430  356.13985  -48.9937624 2933.906
## 328  2013-11-24 1863.518  545.36929  -93.9985201 3080.219
## 329  2013-11-25 1865.607 -599.45476 -141.4684913 1890.014
## 330  2013-11-26 1867.696 -218.55228 -190.8567189 2223.617
## 331  2013-11-27 1869.784 -213.16223 -241.5934994 2180.358
## 332  2013-11-28 1871.873  -29.41662 -293.0975145 2314.689
## 333  2013-11-29 1873.962  159.07673 -344.7870572 2453.581
## 334  2013-11-30 1876.050  356.13985 -396.0910985 2601.429
## 335  2013-12-01 1878.139  545.36929 -446.4599468 2742.378
## 336  2013-12-02 1880.228 -599.45476 -495.3752643 1550.727
## 337  2013-12-03 1882.316 -218.55228 -542.3592240 1886.735
## 338  2013-12-04 1884.405 -213.16223 -586.9826125 1849.590
## 339  2013-12-05 1886.494  -29.41662 -628.8717129 1993.535
## 340  2013-12-06 1888.582  159.07673 -667.7138328 2145.275
## 341  2013-12-07 1890.671  356.13985 -703.2613766 2308.879
## 342  2013-12-08 1892.760  545.36929 -735.3343990 2468.124
## 343  2013-12-09 1894.848 -599.45476 -763.8216135 1296.902
## 344  2013-12-10 1896.937 -218.55228 -788.6798665 1655.035
## 345  2013-12-11 1899.025 -213.16223 -809.9321264 1641.261
## 346  2013-12-12 1901.114  -29.41662 -827.6640702 1809.363
## 347  2013-12-13 1903.203  159.07673 -842.0193845 1985.590
## 348  2013-12-14 1905.291  356.13985 -853.1939243 2173.567
## 349  2013-12-15 1907.380  545.36929 -861.4289009 2356.650
## 350  2013-12-16 1909.469 -599.45476 -867.0032873 1208.341
## 351  2013-12-17 1911.557 -218.55228 -870.2256469 1588.109
## 352  2013-12-18 1913.646 -213.16223 -871.4255986 1594.388
## 353  2013-12-19 1915.735  -29.41662 -870.9451377 1780.703
## 354  2013-12-20 1917.823  159.07673 -869.1300271 1973.100
## 355  2013-12-21 1919.912  356.13985 -866.3214695 2175.060
## 356  2013-12-22 1922.001  545.36929 -862.8482552 2369.852
## 357  2013-12-23 1924.089 -599.45476 -859.0195659 1230.945
## 358  2013-12-24 1926.178 -218.55228 -855.1185906 1617.837
## 359  2013-12-25 1928.267 -213.16223 -851.3970873 1629.037
## 360  2013-12-26 1930.355  -29.41662 -848.0709926 1818.198
## 361  2013-12-27 1932.444  159.07673 -845.3171553 2011.533
## 362  2013-12-28 1934.533  356.13985 -843.2712341 2212.731
## 363  2013-12-29 1936.621  545.36929 -842.0267730 2405.294
## 364  2013-12-30 1938.710 -599.45476 -841.6354302 1262.950
## 365  2013-12-31 1940.799 -218.55228 -842.1083139 1645.468
## 366  2014-01-01 1942.887 -213.16223 -843.4183429 1651.636
## 367  2014-01-02 1944.976  -29.41662 -845.5035310 1835.386
## 368  2014-01-03 1947.065  159.07673 -848.2710686 2023.200
## 369  2014-01-04 1949.153  356.13985 -851.6020590 2219.021
## 370  2014-01-05 1951.242  545.36929 -855.3567530 2406.584
## 371  2014-01-06 1953.330 -599.45476 -859.3801165 1259.825
## 372  2014-01-07 1955.419 -218.55228 -863.5075629 1638.689
## 373  2014-01-08 1957.508 -213.16223 -867.5706802 1642.105
## 374  2014-01-09 1959.596  -29.41662 -871.4027922 1824.107
## 375  2014-01-10 1960.962  159.07673 -874.8441989 2010.525
## 376  2014-01-11 1962.328  356.13985 -877.7469579 2206.051
## 377  2014-01-12 1963.694  545.36929 -879.9790847 2394.414
## 378  2014-01-13 1965.060 -599.45476 -881.4280708 1249.507
## 379  2014-01-14 1966.426 -218.55228 -882.0036408 1631.200
## 380  2014-01-15 1967.792 -213.16223 -881.6396945 1638.320
## 381  2014-01-16 1969.158  -29.41662 -880.2954051 1824.776
## 382  2014-01-17 1970.524  159.07673 -877.9554704 2016.975
## 383  2014-01-18 1971.890  356.13985 -874.6295388 2218.730
## 384  2014-01-19 1973.256  545.36929 -870.3508558 2413.605
## 385  2014-01-20 1974.622 -599.45476 -865.1741980 1275.323
## 386  2014-01-21 1975.988 -218.55228 -859.1731823 1663.593
## 387  2014-01-22 1977.354 -213.16223 -852.4370529 1677.085
## 388  2014-01-23 1978.720  -29.41662 -845.0670627 1869.566
## 389  2014-01-24 1980.086  159.07673 -837.1725745 2067.320
## 390  2014-01-25 1981.452  356.13985 -828.8670129 2274.055
## 391  2014-01-26 1982.818  545.36929 -820.2638000 2473.253
## 392  2014-01-27 1984.184 -599.45476 -811.4724023 1338.587
## 393  2014-01-28 1985.550 -218.55228 -802.5946154 1729.733
## 394  2014-01-29 1986.916 -213.16223 -793.7211968 1745.363
## 395  2014-01-30 1988.282  -29.41662 -784.9289482 1939.266
## 396  2014-01-31 1989.648  159.07673 -776.2783321 2137.776
## 397  2014-02-01 1991.014  356.13985 -767.8116880 2344.672
## 398  2014-02-02 1992.380  545.36929 -759.5520935 2543.527
## 399  2014-02-03 1993.746 -599.45476 -751.5028989 1408.118
## 400  2014-02-04 1995.112 -218.55228 -743.6479355 1798.242
## 401  2014-02-05 1996.478 -213.16223 -735.9523841 1812.693
## 402  2014-02-06 1997.844  -29.41662 -728.3642645 2005.393
## 403  2014-02-07 1999.210  159.07673 -720.8164908 2202.800
## 404  2014-02-08 2000.576  356.13985 -713.2294210 2408.816
## 405  2014-02-09 2001.942  545.36929 -705.5138118 2607.127
## 406  2014-02-10 2003.308 -599.45476 -697.5740825 1471.609
## 407  2014-02-11 2004.674 -218.55228 -689.3117790 1862.140
## 408  2014-02-12 2006.040 -213.16223 -680.6291279 1877.578
## 409  2014-02-13 2007.406  -29.41662 -671.4325660 2071.886
## 410  2014-02-14 2008.772  159.07673 -661.6361343 2271.542
## 411  2014-02-15 2010.138  356.13985 -651.1646299 2480.443
## 412  2014-02-16 2011.504  545.36929 -639.9564179 2682.246
## 413  2014-02-17 2012.870 -599.45476 -627.9658162 1550.779
## 414  2014-02-18 2014.236 -218.55228 -615.1649811 1945.848
## 415  2014-02-19 2015.602 -213.16223 -601.5452359 1966.224
## 416  2014-02-20 2016.968  -29.41662 -587.1178029 2165.763
## 417  2014-02-21 2018.334  159.07673 -571.9139167 2370.826
## 418  2014-02-22 2019.700  356.13985 -555.9843183 2585.185
## 419  2014-02-23 2021.066  545.36929 -539.3981439 2792.367
## 420  2014-02-24 2022.432 -599.45476 -522.2412447 1666.065
## 421  2014-02-25 2023.798 -218.55228 -504.6139884 2065.961
## 422  2014-02-26 2024.219 -213.16223 -486.6286089 2089.758
## 423  2014-02-27 2024.640  -29.41662 -468.4061851 2292.147
## 424  2014-02-28 2025.062  159.07673 -450.0733387 2499.395
## 425  2014-03-01 2025.483  356.13985 -431.7587500 2715.194
## 426  2014-03-02 2025.905  545.36929 -413.5895951 2923.014
## 427  2014-03-03 2026.326 -599.45476 -395.6880104 1796.513
## 428  2014-03-04 2026.747 -218.55228 -378.1676885 2195.357
## 429  2014-03-05 2027.169 -213.16223 -361.1307054 2218.206
## 430  2014-03-06 2027.590  -29.41662 -344.6646719 2418.839
## 431  2014-03-07 2028.012  159.07673 -328.8402924 2623.578
## 432  2014-03-08 2028.433  356.13985 -313.7094010 2836.193
## 433  2014-03-09 2028.854  545.36929 -299.3035325 3040.250
## 434  2014-03-10 2029.276 -599.45476 -285.6330682 1909.518
## 435  2014-03-11 2029.697 -218.55228 -272.6869809 2303.788
## 436  2014-03-12 2030.119 -213.16223 -260.4331860 2321.853
## 437  2014-03-13 2030.540  -29.41662 -248.8194868 2517.634
## 438  2014-03-14 2030.961  159.07673 -237.7750873 2717.593
## 439  2014-03-15 2031.383  356.13985 -227.2126280 2925.640
## 440  2014-03-16 2031.804  545.36929 -217.0306865 3125.473
## 441  2014-03-17 2032.226 -599.45476 -207.1166707 1990.984
## 442  2014-03-18 2032.647 -218.55228 -197.3500237 2382.075
## 443  2014-03-19 2033.068 -213.16223 -187.6056487 2397.630
## 444  2014-03-20 2033.490  -29.41662 -177.7574582 2591.646
## 445  2014-03-21 2033.911  159.07673 -167.6819496 2790.636
## 446  2014-03-22 2034.333  356.13985 -157.2617061 2998.541
## 447  2014-03-23 2034.754  545.36929 -146.3887287 3199.065
## 448  2014-03-24 2035.176 -599.45476 -134.9675081 2066.083
## 449  2014-03-25 2035.597 -218.55228 -122.9177529 2459.457
## 450  2014-03-26 2036.018 -213.16223 -110.1767027 2478.009
## 451  2014-03-27 2036.440  -29.41662  -96.7009653 2675.652
## 452  2014-03-28 2036.861  159.07673  -82.4678315 2878.800
## 453  2014-03-29 2037.283  356.13985  -67.4760354 3091.276
## 454  2014-03-30 2037.704  545.36929  -51.7459441 3296.657
## 455  2014-03-31 2038.125 -599.45476  -35.3191773 2168.681
## 456  2014-04-01 2038.547 -218.55228  -18.2576698 2567.067
## 457  2014-04-02 2038.968 -213.16223   -0.6422098 2590.494
## 458  2014-04-03 2039.390  -29.41662   17.4295055 2792.732
## 459  2014-04-04 2039.811  159.07673   35.8452384 3000.063
## 460  2014-04-05 2040.232  356.13985   54.4809375 3216.183
## 461  2014-04-06 2040.654  545.36929   73.2037459 3424.557
## 462  2014-04-07 2041.075 -599.45476   91.8752090 2298.825
## 463  2014-04-08 2041.497 -218.55228  110.3545945 2698.629
## 464  2014-04-09 2041.918 -213.16223  128.5022382 2722.588
## 465  2014-04-10 2042.339  -29.41662  146.1828263 2924.435
## 466  2014-04-11 2042.761  159.07673  163.2685319 3130.436
## 467  2014-04-12 2043.182  356.13985  179.6419270 3344.294
## 468  2014-04-13 2043.604  545.36929  195.1985977 3549.501
## 469  2014-04-14 2044.025 -599.45476  209.8494033 2419.750
## 470  2014-04-15 2044.446 -218.55228  223.5223266 2814.746
## 471  2014-04-16 2044.868 -213.16223  236.1638775 2833.199
## 472  2014-04-17 2045.289  -29.41662  247.7400244 3028.942
## 473  2014-04-18 2045.711  159.07673  258.2366389 3228.354
## 474  2014-04-19 2046.132  356.13985  267.6594566 3435.261
## 475  2014-04-20 2046.553  545.36929  276.0335642 3633.286
## 476  2014-04-21 2046.975 -599.45476  283.4024413 2496.252
## 477  2014-04-22 2047.396 -218.55228  289.8265906 2884.000
## 478  2014-04-23 2047.818 -213.16223  295.3818045 2895.367
## 479  2014-04-24 2048.239  -29.41662  300.1571211 3084.309
## 480  2014-04-25 2048.660  159.07673  304.2525316 3277.320
## 481  2014-04-26 2049.082  356.13985  307.7765035 3478.328
## 482  2014-04-27 2049.503  545.36929  310.8433878 3671.046
## 483  2014-04-28 2049.925 -599.45476  313.5707788 2529.371
## 484  2014-04-29 2050.346 -218.55228  316.0768946 2913.201
## 485  2014-04-30 2050.767 -213.16223  318.4780404 2921.413
## 486  2014-05-01 2051.189  -29.41662  320.8862168 3107.988
## 487  2014-05-02 2051.610  159.07673  323.4069239 3299.424
## 488  2014-05-03 2052.032  356.13985  326.1372080 3499.639
## 489  2014-05-04 2052.453  545.36929  329.1639884 3692.316
## 490  2014-05-05 2052.875 -599.45476  332.5626921 2551.312
## 491  2014-05-06 2053.296 -218.55228  336.3962145 2936.470
## 492  2014-05-07 2053.717 -213.16223  340.7142162 2946.599
## 493  2014-05-08 2054.139  -29.41662  345.5527557 3135.605
## 494  2014-05-09 2054.560  159.07673  350.9342469 3329.901
## 495  2014-05-10 2054.982  356.13985  356.8677274 3533.319
## 496  2014-05-11 2055.403  545.36929  363.3494094 3729.452
## 497  2014-05-12 2055.824 -599.45476  370.3634856 2592.063
## 498  2014-05-13 2056.246 -218.55228  377.8831530 2980.906
## 499  2014-05-14 2056.667 -213.16223  385.8718162 2994.707
## 500  2014-05-15 2057.089  -29.41662  394.2844282 3187.286
## 501  2014-05-16 2057.510  159.07673  403.0689295 3384.985
## 502  2014-05-17 2057.931  356.13985  412.1677401 3591.569
## 503  2014-05-18 2058.353  545.36929  421.5192696 3790.571
## 504  2014-05-19 2058.774 -599.45476  431.0594047 2655.709
## 505  2014-05-20 2059.196 -218.55228  440.7229449 3046.696
## 506  2014-05-21 2059.617 -213.16223  450.4449554 3062.230
## 507  2014-05-22 2060.038  -29.41662  460.1620163 3256.114
## 508  2014-05-23 2060.460  159.07673  469.8133490 3454.680
## 509  2014-05-24 2060.881  356.13985  479.3418081 3661.693
## 510  2014-05-25 2061.303  545.36929  488.6947329 3860.696
## 511  2014-05-26 2061.724 -599.45476  497.8246543 2725.424
## 512  2014-05-27 2062.145 -218.55228  506.6898633 3115.613
## 513  2014-05-28 2062.567 -213.16223  515.2548445 3129.989
## 514  2014-05-29 2062.988  -29.41662  523.4905863 3322.392
## 515  2014-05-30 2063.410  159.07673  531.3747794 3519.191
## 516  2014-05-31 2063.831  356.13985  538.8919170 3724.193
## 517  2014-06-01 2064.252  545.36929  546.0333105 3920.985
## 518  2014-06-02 2064.674 -599.45476  552.7970343 2783.346
## 519  2014-06-03 2065.095 -218.55228  559.1878122 3171.061
## 520  2014-06-04 2065.517 -213.16223  565.2168557 3182.901
## 521  2014-06-05 2065.938  -29.41662  570.9016623 3372.753
## 522  2014-06-06 2066.359  159.07673  576.2657786 3567.032
## 523  2014-06-07 2066.781  356.13985  581.3385311 3769.589
## 524  2014-06-08 2067.202  545.36929  586.1547232 3964.056
## 525  2014-06-09 2067.624 -599.45476  590.7542943 2824.253
## 526  2014-06-10 2068.045 -218.55228  595.1819349 3210.005
## 527  2014-06-11 2068.466 -213.16223  599.4866494 3220.121
## 528  2014-06-12 2068.888  -29.41662  603.7212544 3408.522
## 529  2014-06-13 2069.309  159.07673  607.9418045 3601.658
## 530  2014-06-14 2069.731  356.13985  612.2069327 3803.407
## 531  2014-06-15 2070.152  545.36929  616.5770961 3997.428
## 532  2014-06-16 2070.574 -599.45476  621.1137195 2857.562
## 533  2014-06-17 2070.995 -218.55228  625.8782320 3243.651
## 534  2014-06-18 2071.416 -213.16223  630.9309944 3254.515
## 535  2014-06-19 2071.838  -29.41662  636.3301216 3444.081
## 536  2014-06-20 2072.259  159.07673  642.1302082 3638.796
## 537  2014-06-21 2072.681  356.13985  648.3809690 3842.531
## 538  2014-06-22 2073.102  545.36929  655.1258161 4038.927
## 539  2014-06-23 2073.523 -599.45476  662.4003954 2901.799
## 540  2014-06-24 2073.945 -218.55228  670.2311131 3290.953
## 541  2014-06-25 2074.366 -213.16223  678.6336873 3305.167
## 542  2014-06-26 2074.788  -29.41662  687.6117629 3498.313
## 543  2014-06-27 2075.209  159.07673  697.1556326 3696.771
## 544  2014-06-28 2075.630  356.13985  707.2411076 3904.341
## 545  2014-06-29 2076.052  545.36929  717.8285833 4104.580
## 546  2014-06-30 2076.473 -599.45476  728.8623434 2971.211
## 547  2014-07-01 2076.895 -218.55228  740.2701445 3363.942
## 548  2014-07-02 2077.316 -213.16223  751.9631199 3381.447
## 549  2014-07-03 2077.737  -29.41662  763.8360339 3577.487
## 550  2014-07-04 2078.159  159.07673  775.7679135 3778.333
## 551  2014-07-05 2078.580  356.13985  787.6230743 3987.673
## 552  2014-07-06 2079.002  545.36929  799.2525502 4188.953
## 553  2014-07-07 2079.423 -599.45476  810.4959223 3055.794
## 554  2014-07-08 2079.844 -218.55228  821.1835371 3447.806
## 555  2014-07-09 2080.266 -213.16223  831.1390862 3463.573
## 556  2014-07-10 2080.687  -29.41662  840.1825147 3656.783
## 557  2014-07-11 2081.109  159.07673  848.1332075 3853.648
## 558  2014-07-12 2081.530  356.13985  854.8134001 4057.813
## 559  2014-07-13 2081.951  545.36929  860.0517419 4252.702
## 560  2014-07-14 2082.373 -599.45476  863.6869405 3111.935
## 561  2014-07-15 2082.794 -218.55228  865.5714028 3495.143
## 562  2014-07-16 2083.216 -213.16223  865.5747868 3500.958
## 563  2014-07-17 2083.637  -29.41662  863.5873745 3683.138
## 564  2014-07-18 2084.058  159.07673  859.5231775 3867.988
## 565  2014-07-19 2084.480  356.13985  853.3226872 4059.272
## 566  2014-07-20 2084.901  545.36929  844.9551885 4240.556
## 567  2014-07-21 2085.323 -599.45476  834.4205603 3085.618
## 568  2014-07-22 2085.744 -218.55228  821.7504989 3454.272
## 569  2014-07-23 2086.166 -213.16223  807.0091105 3445.342
## 570  2014-07-24 2086.587  -29.41662  790.2928308 3612.793
## 571  2014-07-25 2087.008  159.07673  771.7296504 3783.145
## 572  2014-07-26 2087.430  356.13985  751.4776346 3960.377
## 573  2014-07-27 2087.851  545.36929  729.7227496 4128.273
## 574  2014-07-28 2088.273 -599.45476  706.6760203 2960.824
## 575  2014-07-29 2088.694 -218.55228  682.5700664 3318.042
## 576  2014-07-30 2089.115 -213.16223  657.6550776 3298.938
## 577  2014-07-31 2089.537  -29.41662  632.1943070 3457.644
## 578  2014-08-01 2089.958  159.07673  606.4591746 3620.824
## 579  2014-08-02 2090.380  356.13985  580.7240873 3792.573
## 580  2014-08-03 2090.801  545.36929  555.2610897 3956.761
## 581  2014-08-04 2091.222 -599.45476  530.3344694 2787.432
## 582  2014-08-05 2091.644 -218.55228  506.1954432 3144.617
## 583  2014-08-06 2092.065 -213.16223  483.0770530 3127.310
## 584  2014-08-07 2092.487  -29.41662  461.1893974 3289.589
## 585  2014-08-08 2092.908  159.07673  440.7153187 3458.030
## 586  2014-08-09 2093.329  356.13985  421.8066582 3636.606
## 587  2014-08-10 2093.751  545.36929  404.5811777 3809.031
## 588  2014-08-11 2094.172 -599.45476  389.1202329 2649.168
## 589  2014-08-12 2094.594 -218.55228  375.4672649 3016.838
## 590  2014-08-13 2095.015 -213.16223  363.6271582 3010.810
## 591  2014-08-14 2095.436  -29.41662  353.5664897 3184.916
## 592  2014-08-15 2095.858  159.07673  345.2146738 3365.479
## 593  2014-08-16 2096.279  356.13985  338.4659844 3556.215
## 594  2014-08-17 2096.701  545.36929  333.1824100 3740.582
## 595  2014-08-18 2097.122 -599.45476  329.1972810 2592.194
## 596  2014-08-19 2097.543 -218.55228  326.3195805 2970.641
## 597  2014-08-20 2097.965 -213.16223  324.3388388 2974.471
## 598  2014-08-21 2098.386  -29.41662  323.0304879 3157.330
## 599  2014-08-22 2098.808  159.07673  322.1615459 3345.376
## 600  2014-08-23 2099.229  356.13985  321.4964849 3542.195
## 601  2014-08-24 2099.650  545.36929  320.8031346 3731.153
## 602  2014-08-25 2100.072 -599.45476  319.8584679 2585.805
## 603  2014-08-26 2100.493 -218.55228  318.4541193 2965.725
## 604  2014-08-27 2100.915 -213.16223  316.4014894 2969.484
## 605  2014-08-28 2101.336  -29.41662  313.5363022 3150.786
## 606  2014-08-29 2101.758  159.07673  309.7224925 3335.887
## 607  2014-08-30 2102.179  356.13985  304.8553185 3528.504
## 608  2014-08-31 2102.600  545.36929  298.8636160 3712.163
## 609  2014-09-01 2103.022 -599.45476  291.7111306 2560.608
## 610  2014-09-02 2103.443 -218.55228  283.3968919 2933.618
## 611  2014-09-03 2103.865 -213.16223  273.9546167 2929.987
## 612  2014-09-04 2104.286  -29.41662  263.4511561 3103.650
## 613  2014-09-05 2104.707  159.07673  251.9840284 3281.098
## 614  2014-09-06 2105.129  356.13985  239.6781028 3466.277
## 615  2014-09-07 2105.550  545.36929  226.6815261 3642.931
## 616  2014-09-08 2105.972 -599.45476  213.1610030 2485.008
## 617  2014-09-09 2106.393 -218.55228  199.2965623 2852.467
## 618  2014-09-10 2106.814 -213.16223  185.2759552 2844.258
## 619  2014-09-11 2107.236  -29.41662  171.2888434 3014.438
## 620  2014-09-12 2107.657  159.07673  157.5209432 3189.585
## 621  2014-09-13 2108.079  356.13985  144.1482934 3373.697
## 622  2014-09-14 2108.500  545.36929  131.3318132 3550.531
## 623  2014-09-15 2108.921 -599.45476  119.2123101 2394.009
## 624  2014-09-16 2109.343 -218.55228  107.9060872 2764.027
## 625  2014-09-17 2109.764 -213.16223   97.5012815 2759.433
## 626  2014-09-18 2110.186  -29.41662   88.0550499 2934.154
## 627  2014-09-19 2110.607  159.07673   79.5916913 3114.605
## 628  2014-09-20 2111.028  356.13985   72.1017733 3304.600
## 629  2014-09-21 2111.450  545.36929   65.5422991 3487.691
## 630  2014-09-22 2111.871 -599.45476   59.8379259 2337.584
## 631  2014-09-23 2112.293 -218.55228   54.8832110 2713.953
## 632  2014-09-24 2112.714 -213.16223   50.5458370 2715.428
## 633  2014-09-25 2113.135  -29.41662   46.6707358 2895.719
## 634  2014-09-26 2113.557  159.07673   43.0850052 3081.048
## 635  2014-09-27 2113.978  356.13985   39.6034870 3275.051
## 636  2014-09-28 2114.400  545.36929   36.0348566 3461.134
## 637  2014-09-29 2114.821 -599.45476   32.1880527 2312.884
## 638  2014-09-30 2115.243 -218.55228   27.8788682 2689.899
## 639  2014-10-01 2115.664 -213.16223   22.9365121 2690.768
## 640  2014-10-02 2116.085  -29.41662   17.2099493 2869.209
## 641  2014-10-03 2116.507  159.07673   10.5738310 3051.487
## 642  2014-10-04 2116.928  356.13985    2.9338323 3241.332
## 643  2014-10-05 2117.350  545.36929   -5.7687703 3422.280
## 644  2014-10-06 2117.771 -599.45476  -15.5534333 2268.093
## 645  2014-10-07 2118.192 -218.55228  -26.3977201 2638.572
## 646  2014-10-08 2118.614 -213.16223  -38.2358178 2632.546
## 647  2014-10-09 2119.035  -29.41662  -50.9582679 2803.990
## 648  2014-10-10 2119.457  159.07673  -64.4129550 2979.450
## 649  2014-10-11 2119.878  356.13985  -78.4073579 3162.940
## 650  2014-10-12 2120.299  545.36929  -92.7120383 3338.286
## 651  2014-10-13 2120.721 -599.45476 -107.0653064 2179.531
## 652  2014-10-14 2121.142 -218.55228 -121.1789680 2546.741
## 653  2014-10-15 2121.564 -213.16223 -134.7450295 2538.986
## 654  2014-10-16 2121.985  -29.41662 -147.4432075 2710.455
## 655  2014-10-17 2122.406  159.07673 -158.9490637 2887.864
## 656  2014-10-18 2122.816  356.13985 -168.9425697 3075.343
## 657  2014-10-19 2123.226  545.36929 -177.1168852 3256.808
## 658  2014-10-20 2123.636 -599.45476 -183.1871282 2106.324
## 659  2014-10-21 2124.046 -218.55228 -186.8989089 2483.925
## 660  2014-10-22 2124.456 -213.16223 -188.0364011 2488.587
## 661  2014-10-23 2124.866  -29.41662 -186.4297330 2674.349
## 662  2014-10-24 2125.276  159.07673 -181.9614921 2867.721
## 663  2014-10-25 2125.686  356.13985 -174.5721580 3072.583
## 664  2014-10-26 2126.096  545.36929 -164.2643015 3272.530
## 665  2014-10-27 2126.505 -599.45476 -151.1054161 2141.275
## 666  2014-10-28 2126.915 -218.55228 -135.2292801 2538.464
## 667  2014-10-29 2127.325 -213.16223 -116.8357839 2562.657
## 668  2014-10-30 2127.735  -29.41662  -96.1891941 2767.459
## 669  2014-10-31 2128.145  159.07673  -73.6148627 2978.937
## 670  2014-11-01 2128.555  356.13985  -49.4944328 3200.530
## 671  2014-11-02 2128.965  545.36929  -24.2596255 3415.404
## 672  2014-11-03 2129.375 -599.45476    1.6152697 2296.865
## 673  2014-11-04 2129.785 -218.55228   27.6220418 2704.184
## 674  2014-11-05 2130.195 -213.16223   53.2281605 2735.590
## 675  2014-11-06 2130.604  -29.41662   77.8871194 2944.405
## 676  2014-11-07 2131.014  159.07673  101.0492903 3156.470
## 677  2014-11-08 2131.424  356.13985  122.1730415 3375.067
## 678  2014-11-09 2131.834  545.36929  140.7358665 3583.269
## 679  2014-11-10 2132.244 -599.45476  156.2452641 2454.364
## 680  2014-11-11 2132.654 -218.55228  168.2491197 2847.681
## 681  2014-11-12 2133.064 -213.16223  176.3453424 2861.577
## 682  2014-11-13 2133.474  -29.41662  180.1905328 3049.577
## 683  2014-11-14 2133.884  159.07673  179.5074781 3237.798
## 684  2014-11-15 2134.294  356.13985  174.0912958 3429.855
## 685  2014-11-16 2134.703  545.36929  163.8140813 3609.217
## 686  2014-11-17 2135.113 -599.45476  148.6279490 2449.616
## 687  2014-11-18 2135.523 -218.55228  128.5663945 2810.867
## 688  2014-11-19 2135.933 -213.16223  103.7439447 2791.845
## 689  2014-11-20 2136.343  -29.41662   74.3541041 2946.610
## 690  2014-11-21 2136.753  159.07673   40.6656452 3101.825
## 691  2014-11-22 2137.163  356.13985    3.0173297 3261.650
## 692  2014-11-23 2137.573  545.36929  -38.1888150 3410.083
## 693  2014-11-24 2137.983 -599.45476  -82.4955073 2221.362
## 694  2014-11-25 2138.393 -218.55228 -129.3993231 2555.771
## 695  2014-11-26 2138.802 -213.16223 -178.3606962 2512.609
## 696  2014-11-27 2139.212  -29.41662 -228.8145755 2646.311
## 697  2014-11-28 2139.622  159.07673 -280.1814930 2783.847
## 698  2014-11-29 2140.032  356.13985 -331.8787910 2929.623
## 699  2014-11-30 2140.442  545.36929 -383.3317517 3067.809
## 700  2014-12-01 2140.852 -599.45476 -433.9843810 1872.743
## 701  2014-12-02 2141.262 -218.55228 -483.3096072 2204.730
## 702  2014-12-03 2141.543 -213.16223 -530.8186715 2162.892
## 703  2014-12-04 2141.825  -29.41662 -576.0695119 2301.668
## 704  2014-12-05 2142.106  159.07673 -618.6739641 2447.839
## 705  2014-12-06 2142.387  356.13985 -658.3036396 2605.553
## 706  2014-12-07 2142.669  545.36929 -694.6943690 2758.674
## 707  2014-12-08 2142.950 -599.45476 -727.6491395 1581.176
## 708  2014-12-09 2143.232 -218.55228 -757.0394899 1932.970
## 709  2014-12-10 2143.513 -213.16223 -782.8053650 1912.875
## 710  2014-12-11 2143.794  -29.41662 -804.9534696 2074.754
## 711  2014-12-12 2144.076  159.07673 -823.5541962 2244.928
## 712  2014-12-13 2144.357  356.13985 -838.7372348 2427.090
## 713  2014-12-14 2144.639  545.36929 -850.6860019 2604.652
## 714  2014-12-15 2144.920 -599.45476 -859.6310546 1451.164
## 715  2014-12-16 2145.201 -218.55228 -865.8426728 1826.136
## 716  2014-12-17 2145.483 -213.16223 -869.6228118 1828.028
## 717  2014-12-18 2145.764  -29.41662 -871.2966385 2010.381
## 718  2014-12-19 2146.045  159.07673 -871.2038675 2199.248
## 719  2014-12-20 2146.327  356.13985 -869.6901149 2398.106
## 720  2014-12-21 2146.608  545.36929 -867.0984815 2590.209
## 721  2014-12-22 2146.890 -599.45476 -863.7615637 1449.003
## 722  2014-12-23 2147.171 -218.55228 -859.9940782 1833.955
## 723  2014-12-24 2147.452 -213.16223 -856.0862609 1843.534
## 724  2014-12-25 2147.734  -29.41662 -852.2981816 2031.349
## 725  2014-12-26 2148.015  159.07673 -848.8550834 2223.567
## 726  2014-12-27 2148.297  356.13985 -845.9438299 2423.822
## 727  2014-12-28 2148.578  545.36929 -843.7105100 2615.567
## 728  2014-12-29 2148.859 -599.45476 -842.2592193 1472.475
## 729  2014-12-30 2149.141 -218.55228 -841.6520043 1854.266
## 730  2014-12-31 2149.422 -213.16223 -841.9099279 1859.680
## 731  2015-01-01 2149.704  -29.41662 -843.0151824 2042.602
## 732  2015-01-02 2149.985  159.07673 -844.9141540 2229.477
## 733  2015-01-03 2150.266  356.13985 -847.5213180 2424.215
## 734  2015-01-04 2150.548  545.36929 -850.7238253 2610.523
## 735  2015-01-05 2150.829 -599.45476 -854.3866281 1462.318
## 736  2015-01-06 2151.111 -218.55228 -858.3579796 1839.530
## 737  2015-01-07 2151.392 -213.16223 -862.4751413 1841.084
## 738  2015-01-08 2151.673  -29.41662 -866.5701271 2021.016
## 739  2015-01-09 2151.955  159.07673 -870.4753206 2205.886
## 740  2015-01-10 2152.236  356.13985 -874.0288091 2399.677
## 741  2015-01-11 2152.517  545.36929 -877.0792926 2586.137
## 742  2015-01-12 2152.799 -599.45476 -879.4904391 1439.184
## 743  2015-01-13 2153.080 -218.55228 -881.1445818 1818.713
## 744  2015-01-14 2153.362 -213.16223 -881.9456723 1823.584
## 745  2015-01-15 2153.643  -29.41662 -881.8214307 2007.735
## 746  2015-01-16 2153.924  159.07673 -880.7246551 2197.606
## 747  2015-01-17 2154.206  356.13985 -878.6336845 2397.042
## 748  2015-01-18 2154.487  545.36929 -875.5520270 2589.634
## 749  2015-01-19 2154.769 -599.45476 -871.5071961 1449.137
## 750  2015-01-20 2155.050 -218.55228 -866.5488150 1835.279
## 751  2015-01-21 2155.331 -213.16223 -860.7460735 1846.753
## 752  2015-01-22 2155.613  -29.41662 -854.1846342 2037.341
## 753  2015-01-23 2155.894  159.07673 -846.9631047 2233.338
## 754  2015-01-24 2156.176  356.13985 -839.1891963 2438.456
## 755  2015-01-25 2156.457  545.36929 -830.9757008 2636.180
## 756  2015-01-26 2156.738 -599.45476 -822.4364180 1500.177
## 757  2015-01-27 2157.020 -218.55228 -813.6821629 1890.115
## 758  2015-01-28 2157.301 -213.16223 -804.8169800 1904.652
## 759  2015-01-29 2157.583  -29.41662 -795.9346789 2097.561
## 760  2015-01-30 2157.864  159.07673 -787.1157958 2295.155
## 761  2015-01-31 2158.145  356.13985 -778.4250699 2501.190
## 762  2015-02-01 2158.427  545.36929 -769.9095036 2699.216
## 763  2015-02-02 2158.708 -599.45476 -761.5970604 1562.986
## 764  2015-02-03 2158.990 -218.55228 -753.4960291 1952.271
## 765  2015-02-04 2159.271 -213.16223 -745.5950645 1965.843
## 766  2015-02-05 2159.552  -29.41662 -737.8638939 2157.602
## 767  2015-02-06 2159.834  159.07673 -730.2546556 2353.986
## 768  2015-02-07 2160.115  356.13985 -722.7038191 2558.881
## 769  2015-02-08 2160.396  545.36929 -715.1346186 2755.961
## 770  2015-02-09 2160.678 -599.45476 -707.4599155 1619.093
## 771  2015-02-10 2160.959 -218.55228 -699.5853945 2008.151
## 772  2015-02-11 2161.241 -213.16223 -691.4129883 2021.995
## 773  2015-02-12 2161.522  -29.41662 -682.8444195 2214.591
## 774  2015-02-13 2161.803  159.07673 -673.7847471 2412.425
## 775  2015-02-14 2162.085  356.13985 -664.1458043 2619.409
## 776  2015-02-15 2162.366  545.36929 -653.8494207 2819.216
## 777  2015-02-16 2162.648 -599.45476 -642.8303277 1685.692
## 778  2015-02-17 2162.929 -218.55228 -631.0386577 2078.668
## 779  2015-02-18 2163.210 -213.16223 -618.4419603 2096.936
## 780  2015-02-19 2163.492  -29.41662 -605.0266747 2294.378
## 781  2015-02-20 2163.773  159.07673 -590.7990132 2497.381
## 782  2015-02-21 2164.055  356.13985 -575.7852308 2709.739
## 783  2015-02-22 2164.336  545.36929 -560.0312730 2915.004
## 784  2015-02-23 2164.617 -599.45476 -543.6018132 1786.891
## 785  2015-02-24 2164.899 -218.55228 -526.5787108 2185.098
## 786  2015-02-25 2165.180 -213.16223 -509.0589362 2208.289
## 787  2015-02-26 2165.462  -29.41662 -491.1520272 2410.223
## 788  2015-02-27 2165.743  159.07673 -472.9771518 2617.172
## 789  2015-02-28 2166.024  356.13985 -454.6598670 2832.834
## 790  2015-03-01 2166.306  545.36929 -436.3286714 3040.676
## 791  2015-03-02 2166.587 -599.45476 -418.1114513 1914.351
## 792  2015-03-03 2166.869 -218.55228 -400.1319292 2313.514
## 793  2015-03-04 2167.150 -213.16223 -382.5062167 2336.811
## 794  2015-03-05 2167.431  -29.41662 -365.3395752 2538.005
## 795  2015-03-06 2167.713  159.07673 -348.7234779 2743.396
## 796  2015-03-07 2167.994  356.13985 -332.7330597 2956.731
## 797  2015-03-08 2168.275  545.36929 -317.4250278 3161.550
## 798  2015-03-09 2168.557 -599.45476 -302.8360950 2031.596
## 799  2015-03-10 2168.838 -218.55228 -288.9819785 2426.634
## 800  2015-03-11 2169.120 -213.16223 -275.8569940 2445.430
## 801  2015-03-12 2169.401  -29.41662 -263.4342554 2641.880
## 802  2015-03-13 2169.682  159.07673 -251.6664739 2842.423
## 803  2015-03-14 2169.964  356.13985 -240.4873318 3050.946
## 804  2015-03-15 2170.245  545.36929 -229.8133931 3251.131
## 805  2015-03-16 2170.527 -599.45476 -219.5464940 2116.855
## 806  2015-03-17 2170.808 -218.55228 -209.5765450 2508.009
## 807  2015-03-18 2171.089 -213.16223 -199.7846664 2523.472
## 808  2015-03-19 2171.371  -29.41662 -190.0465666 2717.237
## 809  2015-03-20 2171.652  159.07673 -180.2360701 2915.823
## 810  2015-03-21 2171.934  356.13985 -170.2286952 3123.175
## 811  2015-03-22 2172.215  545.36929 -159.9051830 3323.009
## 812  2015-03-23 2172.496 -599.45476 -149.1548805 2189.217
## 813  2015-03-24 2172.778 -218.55228 -137.8788854 2581.676
## 814  2015-03-25 2173.059 -213.16223 -125.9928677 2599.234
## 815  2015-03-26 2173.341  -29.41662 -113.4294924 2795.824
## 816  2015-03-27 2173.622  159.07673 -100.1403811 2997.888
## 817  2015-03-28 2173.903  356.13985  -86.0975604 3209.275
## 818  2015-03-29 2174.185  545.36929  -71.2943633 3413.590
## 819  2015-03-30 2174.466 -599.45476  -55.7457623 2284.595
## 820  2015-03-31 2174.747 -218.55228  -39.4881305 2682.037
## 821  2015-04-01 2175.029 -213.16223  -22.5784410 2704.618
## 822  2015-04-02 2175.310  -29.41662   -5.0929331 2906.131
## 823  2015-04-03 2175.592  159.07673   12.8747167 3112.873
## 824  2015-04-04 2175.873  356.13985   31.2156631 3328.558
## 825  2015-04-05 2176.154  545.36929   49.8085356 3536.662
## 826  2015-04-06 2176.436 -599.45476   68.5223843 2410.833
## 827  2015-04-07 2176.717 -218.55228   87.2198457 2810.715
## 828  2015-04-08 2176.999 -213.16223  105.7604428 2834.927
## 829  2015-04-09 2177.280  -29.41662  124.0039326 3037.197
## 830  2015-04-10 2177.561  159.07673  141.8136125 3243.782
## 831  2015-04-11 2177.843  356.13985  159.0595010 3458.372
## 832  2015-04-12 2178.124  545.36929  175.6213124 3664.445
## 833  2015-04-13 2178.406 -599.45476  191.3911527 2535.672
## 834  2015-04-14 2178.687 -218.55228  206.2758726 2931.740
## 835  2015-04-15 2178.968 -213.16223  220.1990245 2951.335
## 836  2015-04-16 2179.250  -29.41662  233.1023805 3148.265
## 837  2015-04-17 2179.531  159.07673  244.9469834 3348.885
## 838  2015-04-18 2179.813  356.13985  255.7137141 3556.996
## 839  2015-04-19 2180.094  545.36929  265.4033719 3756.196
## 840  2015-04-20 2180.375 -599.45476  274.0362789 2620.287
## 841  2015-04-21 2180.657 -218.55228  281.6514295 3009.086
## 842  2015-04-22 2180.963 -213.16223  288.3052197 3021.436
## 843  2015-04-23 2181.269  -29.41662  294.0698000 3211.252
## 844  2015-04-24 2181.575  159.07673  299.0311035 3405.013
## 845  2015-04-25 2181.882  356.13985  303.2866091 3606.638
## 846  2015-04-26 2182.188  545.36929  306.9429051 3799.830
## 847  2015-04-27 2182.494 -599.45476  310.1131183 2658.482
## 848  2015-04-28 2182.800 -218.55228  312.9142799 3042.492
## 849  2015-04-29 2183.106 -213.16223  315.4646939 3050.739
## 850  2015-04-30 2183.413  -29.41662  317.8813749 3237.207
## 851  2015-05-01 2183.719  159.07673  320.2776137 3428.403
## 852  2015-05-02 2184.025  356.13985  322.7607289 3628.255
## 853  2015-05-03 2184.331  545.36929  325.4300487 3820.460
## 854  2015-05-04 2184.637 -599.45476  328.3751645 2678.888
## 855  2015-05-05 2184.944 -218.55228  331.6744868 3063.396
## 856  2015-05-06 2185.250 -213.16223  335.3941230 3072.812
## 857  2015-05-07 2185.556  -29.41662  339.5870899 3261.056
## 858  2015-05-08 2185.862  159.07673  344.2928629 3454.562
## 859  2015-05-09 2186.168  356.13985  349.5372538 3657.175
## 860  2015-05-10 2186.475  545.36929  355.3326030 3852.506
## 861  2015-05-11 2186.781 -599.45476  361.6782630 2714.334
## 862  2015-05-12 2187.087 -218.55228  368.5613432 3102.426
## 863  2015-05-13 2187.393 -213.16223  375.9576832 3115.519
## 864  2015-05-14 2187.699  -29.41662  383.8330143 3307.446
## 865  2015-05-15 2188.006  159.07673  392.1442711 3504.557
## 866  2015-05-16 2188.312  356.13985  400.8410083 3710.623
## 867  2015-05-17 2188.618  545.36929  409.8668848 3909.184
## 868  2015-05-18 2188.924 -599.45476  419.1611716 2773.961
## 869  2015-05-19 2189.230 -218.55228  428.6602492 3164.668
## 870  2015-05-20 2189.537 -213.16223  438.2990584 3180.003
## 871  2015-05-21 2189.843  -29.41662  448.0124764 3373.769
## 872  2015-05-22 2190.149  159.07673  457.7365939 3572.292
## 873  2015-05-23 2190.455  356.13985  467.4098736 3779.335
## 874  2015-05-24 2190.761  545.36929  476.9741764 3978.435
## 875  2015-05-25 2191.068 -599.45476  486.3756485 2843.318
## 876  2015-05-26 2191.374 -218.55228  495.5654644 3233.717
## 877  2015-05-27 2191.680 -213.16223  504.5004293 3248.348
## 878  2015-05-28 2191.986  -29.41662  513.1434455 3441.043
## 879  2015-05-29 2192.293  159.07673  521.4638529 3638.163
## 880  2015-05-30 2192.599  356.13985  529.4376535 3843.506
## 881  2015-05-31 2192.905  545.36929  537.0476355 4040.652
## 882  2015-06-01 2193.211 -599.45476  544.2834081 2903.370
## 883  2015-06-02 2193.517 -218.55228  551.1413638 3291.436
## 884  2015-06-03 2193.824 -213.16223  557.6245773 3303.616
## 885  2015-06-04 2194.130  -29.41662  563.7426559 3493.786
## 886  2015-06-05 2194.436  159.07673  569.5115461 3688.354
## 887  2015-06-06 2194.742  356.13985  574.9533065 3891.165
## 888  2015-06-07 2195.048  545.36929  580.0958456 4085.843
## 889  2015-06-08 2195.449 -599.45476  584.9726279 2946.297
## 890  2015-06-09 2195.850 -218.55228  589.6223430 3332.250
## 891  2015-06-10 2196.252 -213.16223  594.0885326 3342.508
## 892  2015-06-11 2196.653  -29.41662  598.4191667 3530.985
## 893  2015-06-12 2197.054  159.07673  602.6661599 3724.126
## 894  2015-06-13 2197.455  356.13985  606.8848155 3925.809
## 895  2015-06-14 2197.856  545.36929  611.1331888 4119.688
## 896  2015-06-15 2198.257 -599.45476  615.4713569 2979.603
## 897  2015-06-16 2198.658 -218.55228  619.9605890 3365.396
## 898  2015-06-17 2199.059 -213.16223  624.6624093 3375.889
## 899  2015-06-18 2199.460  -29.41662  629.6375521 3565.011
## 900  2015-06-19 2199.861  159.07673  634.9448098 3759.213
## 901  2015-06-20 2200.262  356.13985  640.6397813 3962.372
## 902  2015-06-21 2200.663  545.36929  646.7735326 4158.136
## 903  2015-06-22 2201.064 -599.45476  653.3911878 3020.331
## 904  2015-06-23 2201.465 -218.55228  660.5304724 3408.773
## 905  2015-06-24 2201.866 -213.16223  668.2202401 3422.254
## 906  2015-06-25 2202.267  -29.41662  676.4790141 3614.660
## 907  2015-06-26 2202.669  159.07673  685.3135822 3812.389
## 908  2015-06-27 2203.070  356.13985  694.7176877 4019.257
## 909  2015-06-28 2203.471  545.36929  704.6708583 4218.841
## 910  2015-06-29 2203.872 -599.45476  715.1374185 3084.884
## 911  2015-06-30 2204.273 -218.55228  726.0657305 3477.116
## 912  2015-07-01 2204.674 -213.16223  737.3877048 3494.229
## 913  2015-07-02 2205.075  -29.41662  749.0186209 3690.007
## 914  2015-07-03 2205.476  159.07673  760.8572912 3890.740
## 915  2015-07-04 2205.877  356.13985  772.7865964 4100.133
## 916  2015-07-05 2206.278  545.36929  784.6744119 4301.652
## 917  2015-07-06 2206.679 -599.45476  796.3749359 3168.929
## 918  2015-07-07 2207.080 -218.55228  807.7304196 3561.588
## 919  2015-07-08 2207.481 -213.16223  818.5732900 3578.222
## 920  2015-07-09 2207.882  -29.41662  828.7286419 3772.524
## 921  2015-07-10 2208.283  159.07673  838.0170681 3970.707
## 922  2015-07-11 2208.684  356.13985  846.2577816 4176.412
## 923  2015-07-12 2209.086  545.36929  853.2719758 4373.057
## 924  2015-07-13 2209.487 -599.45476  858.8863569 3234.248
## 925  2015-07-14 2209.888 -218.55228  862.9367750 3619.602
## 926  2015-07-15 2210.289 -213.16223  865.2718742 3627.728
## 927  2015-07-16 2210.690  -29.41662  865.7566749 3812.360
## 928  2015-07-17 2211.091  159.07673  864.2760000 3999.773
## 929  2015-07-18 2211.492  356.13985  860.7376556 4193.699
## 930  2015-07-19 2211.893  545.36929  855.0752779 4377.667
## 931  2015-07-20 2212.294 -599.45476  847.2507633 3225.420
## 932  2015-07-21 2212.695 -218.55228  837.2562039 3596.729
## 933  2015-07-22 2213.096 -213.16223  825.1152609 3590.379
## 934  2015-07-23 2213.497  -29.41662  810.8839184 3760.294
## 935  2015-07-24 2213.898  159.07673  794.6505751 3932.955
## 936  2015-07-25 2214.434  356.13985  776.5354442 4112.439
## 937  2015-07-26 2214.969  545.36929  756.6892492 4282.357
## 938  2015-07-27 2215.504 -599.45476  735.2912222 3116.671
## 939  2015-07-28 2216.040 -218.55228  712.5464247 3475.364
## 940  2015-07-29 2216.575 -213.16223  688.6824343 3457.425
## 941  2015-07-30 2217.110  -29.41662  663.9454536 3616.969
## 942  2015-07-31 2217.645  159.07673  638.5959151 3780.648
## 943  2015-08-01 2218.181  356.13985  612.9036737 3952.554
## 944  2015-08-02 2218.716  545.36929  587.1428863 4116.558
## 945  2015-08-03 2219.251 -599.45476  561.5866944 2946.713
## 946  2015-08-04 2219.787 -218.55228  536.5018284 3303.066
## 947  2015-08-05 2220.322 -213.16223  512.1432615 3284.633
## 948  2015-08-06 2220.857  -29.41662  488.7490417 3445.520
## 949  2015-08-07 2221.393  159.07673  466.5354275 3612.335
## 950  2015-08-08 2221.928  356.13985  445.6924505 3789.090
## 951  2015-08-09 2222.463  545.36929  426.3800182 3959.542
## 952  2015-08-10 2222.998 -599.45476  408.7246612 2797.598
## 953  2015-08-11 2223.534 -218.55228  392.8170110 3163.128
## 954  2015-08-12 2224.069 -213.16223  378.7100822 3154.947
## 955  2015-08-13 2224.604  -29.41662  366.4184099 3326.936
## 956  2015-08-14 2225.140  159.07673  355.9180755 3505.464
## 957  2015-08-15 2225.675  356.13985  347.1476282 3694.292
## 958  2015-08-16 2226.210  545.36929  340.0098909 3876.919
## 959  2015-08-17 2226.746 -599.45476  334.3746124 2726.995
## 960  2015-08-18 2227.281 -218.55228  330.0819083 3104.140
## 961  2015-08-19 2227.816 -213.16223  326.9464108 3106.930
## 962  2015-08-20 2228.351  -29.41662  324.7620270 3289.027
## 963  2015-08-21 2228.887  159.07673  323.3071912 3476.601
## 964  2015-08-22 2229.422  356.13985  322.3504794 3673.242
## 965  2015-08-23 2229.957  545.36929  321.6564456 3862.313
## 966  2015-08-24 2230.493 -599.45476  320.9915304 2717.359
## 967  2015-08-25 2231.028 -218.55228  320.1298908 3097.935
## 968  2015-08-26 2231.563 -213.16223  318.8589985 3102.590
## 969  2015-08-27 2232.099  -29.41662  316.9848619 3284.997
## 970  2015-08-28 2232.634  159.07673  314.3367316 3471.377
## 971  2015-08-29 2233.169  356.13985  310.7711660 3665.410
## 972  2015-08-30 2233.705  545.36929  306.1753464 3850.579
## 973  2015-08-31 2234.240 -599.45476  300.4695524 2700.584
## 974  2015-09-01 2234.775 -218.55228  293.6087292 3075.161
## 975  2015-09-02 2235.310 -213.16223  285.5831036 3073.061
## 976  2015-09-03 2235.846  -29.41662  276.4178292 3248.177
## 977  2015-09-04 2236.381  159.07673  266.1716701 3426.959
## 978  2015-09-05 2236.916  356.13985  254.9347569 3613.321
## 979  2015-09-06 2237.452  545.36929  242.8254752 3790.976
## 980  2015-09-07 2237.987 -599.45476  229.9865717 2633.849
## 981  2015-09-08 2238.522 -218.55228  216.5805845 3001.880
## 982  2015-09-09 2239.302 -213.16223  202.7847249 2994.254
## 983  2015-09-10 2240.081  -29.41662  188.7853529 3164.780
## 984  2015-09-11 2240.861  159.07673  174.7722027 3340.040
## 985  2015-09-12 2241.641  356.13985  160.9325222 3524.043
## 986  2015-09-13 2242.420  545.36929  147.4452937 3700.565
## 987  2015-09-14 2243.200 -599.45476  134.4757045 2543.550
## 988  2015-09-15 2243.979 -218.55228  122.1700279 2912.927
## 989  2015-09-16 2244.759 -213.16223  110.6510669 2907.577
## 990  2015-09-17 2245.538  -29.41662  100.0142988 3081.466
## 991  2015-09-18 2246.318  159.07673   90.3248393 3261.049
## 992  2015-09-19 2247.097  356.13985   81.6153239 3450.182
## 993  2015-09-20 2247.877  545.36929   73.8847783 3632.461
## 994  2015-09-21 2248.657 -599.45476   67.0985236 2481.630
## 995  2015-09-22 2249.436 -218.55228   61.1891325 2857.403
## 996  2015-09-23 2250.216 -213.16223   56.0584219 2858.442
## 997  2015-09-24 2250.995  -29.41662   51.5804399 3038.489
## 998  2015-09-25 2251.775  159.07673   47.6053742 3223.787
## 999  2015-09-26 2252.554  356.13985   43.9642814 3417.988
## 1000 2015-09-27 2253.334  545.36929   40.4745139 3604.508
## 1001 2015-09-28 2254.114 -599.45476   36.9456959 2456.934
## 1002 2015-09-29 2254.893 -218.55228   33.1860855 2834.857
## 1003 2015-09-30 2255.673 -213.16223   29.0091427 2836.849
## 1004 2015-10-01 2256.452  -29.41662   24.2401159 3016.606
## 1005 2015-10-02 2257.232  159.07673   18.7224560 3200.361
## 1006 2015-10-03 2258.011  356.13985   12.3238660 3391.805
## 1007 2015-10-04 2258.791  545.36929    4.9418035 3574.432
## 1008 2015-10-05 2259.570 -599.45476   -3.4917369 2421.954
## 1009 2015-10-06 2260.350 -218.55228  -13.0063173 2794.121
## 1010 2015-10-07 2261.130 -213.16223  -23.5901596 2789.707
## 1011 2015-10-08 2261.909  -29.41662  -35.1883685 2962.634
## 1012 2015-10-09 2262.689  159.07673  -47.7023539 3139.393
## 1013 2015-10-10 2263.468  356.13985  -60.9905025 3323.947
## 1014 2015-10-11 2264.248  545.36929  -74.8701151 3500.077
## 1015 2015-10-12 2265.027 -599.45476  -89.1205901 2341.782
## 1016 2015-10-13 2265.807 -218.55228 -103.4878019 2709.097
## 1017 2015-10-14 2266.587 -213.16223 -117.6895888 2701.065
## 1018 2015-10-15 2267.366  -29.41662 -131.4222317 2871.857
## 1019 2015-10-16 2268.146  159.07673 -144.3677782 3048.184
## 1020 2015-10-17 2268.925  356.13985 -156.2020389 3234.193
## 1021 2015-10-18 2269.705  545.36929 -166.6030647 3413.801
## 1022 2015-10-19 2270.484 -599.45476 -175.2598917 2261.100
## 1023 2015-10-20 2271.264 -218.55228 -181.8813352 2636.160
## 1024 2015-10-21 2272.043 -213.16223 -186.2046038 2638.006
## 1025 2015-10-22 2272.823  -29.41662 -188.0035074 2820.733
## 1026 2015-10-23 2273.603  159.07673 -187.0960378 3010.913
## 1027 2015-10-24 2274.382  356.13985 -183.3511133 3212.501
## 1028 2015-10-25 2275.162  545.36929 -176.6942962 3409.167
## 1029 2015-10-26 2275.999 -599.45476 -167.1123137 2274.762
## 1030 2015-10-27 2276.837 -218.55228 -154.6562420 2668.958
## 1031 2015-10-28 2277.674 -213.16223 -139.4432438 2690.398
## 1032 2015-10-29 2278.511  -29.41662 -121.6567831 2892.768
## 1033 2015-10-30 2279.349  159.07673 -101.5452804 3102.210
## 1034 2015-10-31 2280.186  356.13985  -79.4192086 3322.237
## 1035 2015-11-01 2281.023  545.36929  -55.6466668 3536.076
## 1036 2015-11-02 2281.861 -599.45476  -30.6475124 2417.088
## 1037 2015-11-03 2282.698 -218.55228   -4.8861620 2824.590
## 1038 2015-11-04 2283.536 -213.16223   21.1367874 2856.840
## 1039 2015-11-05 2284.373  -29.41662   46.8939409 3067.180
## 1040 2015-11-06 2285.210  159.07673   71.8412844 3281.458
## 1041 2015-11-07 2286.048  356.13985   95.4289336 3502.947
## 1042 2015-11-08 2286.885  545.36929  117.1122106 3714.697
## 1043 2015-11-09 2287.723 -599.45476  136.3627933 2589.961
## 1044 2015-11-10 2288.560 -218.55228  152.6796824 2988.017
## 1045 2015-11-11 2289.397 -213.16223  165.5997299 3007.165
## 1046 2015-11-12 2290.235  -29.41662  174.7074849 3200.856
## 1047 2015-11-13 2291.072  159.07673  179.6441234 3395.123
## 1048 2015-11-14 2291.910  356.13985  180.1152546 3593.495
## 1049 2015-11-15 2292.747  545.36929  175.8974168 3779.344
## 1050 2015-11-16 2293.584 -599.45476  166.8431118 2626.303
## 1051 2015-11-17 2294.422 -218.55228  152.8842549 2994.084
## 1052 2015-11-18 2295.259 -213.16223  134.0339622 2981.461
## 1053 2015-11-19 2296.097  -29.41662  110.3866294 3142.397
## 1054 2015-11-20 2296.934  159.07673   82.1163007 3303.457
## 1055 2015-11-21 2297.771  356.13985   49.4733671 3468.715
## 1056 2015-11-22 2298.609  545.36929   12.7796693 3622.088
## 1057 2015-11-23 2299.446 -599.45476  -27.5778778 2437.743
## 1058 2015-11-24 2300.284 -218.55228  -71.1549916 2775.906
## 1059 2015-11-25 2301.121 -213.16223 -117.4588770 2735.830
## 1060 2015-11-26 2301.958  -29.41662 -165.9580257 2871.914
## 1061 2015-11-27 2302.796  159.07673 -216.0927319 3011.110
## 1062 2015-11-28 2303.633  356.13985 -267.2860813 3157.817
## 1063 2015-11-29 2304.471  545.36929 -318.9551620 3296.215
## 1064 2015-11-30 2305.308 -599.45476 -370.5222424 2100.661
## 1065 2015-12-01 2306.145 -218.55228 -421.4256648 2431.497
## 1066 2015-12-02 2306.983 -213.16223 -471.1302111 2388.020
## 1067 2015-12-03 2307.820  -29.41662 -519.1367161 2524.597
## 1068 2015-12-04 2308.658  159.07673 -564.9907193 2668.074
## 1069 2015-12-05 2309.495  356.13985 -608.2899773 2822.675
## 1070 2015-12-06 2310.332  545.36929 -648.6906833 2972.341
## 1071 2015-12-07 2311.170 -599.45476 -685.9122783 1791.133
## 1072 2015-12-08 2312.007 -218.55228 -719.7407688 2139.044
## 1073 2015-12-09 2312.845 -213.16223 -750.0305097 2114.982
## 1074 2015-12-10 2313.682  -29.41662 -776.7044410 2272.891
## 1075 2015-12-11 2314.519  159.07673 -799.7528114 2439.173
## 1076 2015-12-12 2315.370  356.13985 -819.2304538 2617.609
## 1077 2015-12-13 2316.221  545.36929 -835.2527123 2791.667
## 1078 2015-12-14 2317.072 -599.45476 -847.9901529 1634.957
## 1079 2015-12-15 2317.922 -218.55228 -857.6622138 2007.038
## 1080 2015-12-16 2318.773 -213.16223 -864.5299774 2006.411
## 1081 2015-12-17 2319.624  -29.41662 -868.8882612 2186.649
## 1082 2015-12-18 2320.475  159.07673 -871.0572374 2373.824
## 1083 2015-12-19 2321.325  356.13985 -871.3737984 2571.421
## 1084 2015-12-20 2322.176  545.36929 -870.1828868 2762.692
## 1085 2015-12-21 2323.027 -599.45476 -867.8290010 1621.073
## 1086 2015-12-22 2323.877 -218.55228 -864.6480819 2006.007
## 1087 2015-12-23 2324.728 -213.16223 -860.9599678 2015.936
## 1088 2015-12-24 2325.579  -29.41662 -857.0615857 2204.431
## 1089 2015-12-25 2326.430  159.07673 -853.2210254 2397.615
## 1090 2015-12-26 2327.280  356.13985 -849.6726143 2599.077
## 1091 2015-12-27 2328.131  545.36929 -846.6130811 2792.217
## 1092 2015-12-28 2328.982 -599.45476 -844.1988688 1650.658
## 1093 2015-12-29 2329.833 -218.55228 -842.5446211 2034.065
## 1094 2015-12-30 2330.683 -213.16223 -841.7228400 2041.128
## 1095 2015-12-31 2331.534  -29.41662 -841.7646755 2225.683
## 1096 2016-01-01 2332.385  159.07673 -842.6617855 2414.130
## 1097 2016-01-02 2333.235  356.13985 -844.3691729 2610.336
## 1098 2016-01-03 2334.086  545.36929 -846.8088850 2797.976
## 1099 2016-01-04 2334.937 -599.45476 -849.8744418 1650.938
## 1100 2016-01-05 2335.788 -218.55228 -853.4358412 2029.129
## 1101 2016-01-06 2336.638 -213.16223 -857.3449814 2031.461
## 1102 2016-01-07 2337.489  -29.41662 -861.4413318 2211.961
## 1103 2016-01-08 2338.340  159.07673 -865.5576839 2397.189
## 1104 2016-01-09 2339.191  356.13985 -869.5258152 2591.134
## 1105 2016-01-10 2340.041  545.36929 -873.1819080 2777.558
## 1106 2016-01-11 2340.892 -599.45476 -876.3715772 1630.395
## 1107 2016-01-12 2341.743 -218.55228 -878.9543748 2009.566
## 1108 2016-01-13 2342.593 -213.16223 -880.8076604 2013.953
## 1109 2016-01-14 2343.444  -29.41662 -881.8297477 2197.528
## 1110 2016-01-15 2344.295  159.07673 -881.9422582 2386.759
## 1111 2016-01-16 2345.146  356.13985 -881.0916445 2585.524
## 1112 2016-01-17 2345.996  545.36929 -879.2498629 2777.446
## 1113 2016-01-18 2346.847 -599.45476 -876.4142085 1636.308
## 1114 2016-01-19 2347.698 -218.55228 -872.6063436 2021.869
## 1115 2016-01-20 2348.549 -213.16223 -867.8705789 2032.846
## 1116 2016-01-21 2349.399  -29.41662 -862.2714826 2223.041
## 1117 2016-01-22 2350.250  159.07673 -855.8909153 2418.766
## 1118 2016-01-23 2351.101  356.13985 -848.8245983 2623.746
## 1119 2016-01-24 2351.951  545.36929 -841.1783391 2821.472
## 1120 2016-01-25 2352.802 -599.45476 -833.0640417 1685.613
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## 1122 2016-01-27 2354.504 -213.16223 -815.8850408 2090.786
## 1123 2016-01-28 2355.354  -29.41662 -807.0383399 2284.229
## 1124 2016-01-29 2356.205  159.07673 -798.1522021 2482.459
## 1125 2016-01-30 2357.056  356.13985 -789.3107404 2689.215
## 1126 2016-01-31 2357.907  545.36929 -780.5828485 2888.023
## 1127 2016-02-01 2358.757 -599.45476 -772.0201110 1752.612
## 1128 2016-02-02 2359.608 -218.55228 -763.6553369 2142.730
## 1129 2016-02-03 2360.459 -213.16223 -755.5017563 2157.125
## 1130 2016-02-04 2361.309  -29.41662 -747.5528919 2349.670
## 1131 2016-02-05 2362.160  159.07673 -739.7831014 2546.784
## 1132 2016-02-06 2363.011  356.13985 -732.1487618 2752.332
## 1133 2016-02-07 2363.862  545.36929 -724.5900506 2949.971
## 1134 2016-02-08 2364.712 -599.45476 -717.0332576 1813.554
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## 1136 2016-02-10 2366.414 -213.16223 -701.5780897 2217.003
## 1137 2016-02-11 2367.264  -29.41662 -693.4894211 2409.688
## 1138 2016-02-12 2368.115  159.07673 -685.0289840 2607.493
## 1139 2016-02-13 2368.966  356.13985 -676.1006748 2814.335
## 1140 2016-02-14 2369.817  545.36929 -666.6143210 3013.902
## 1141 2016-02-15 2370.667 -599.45476 -656.4889666 1880.054
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## 1146 2016-02-20 2374.921  356.13985 -594.4309944 2901.960
## 1147 2016-02-21 2375.772  545.36929 -579.6101922 3106.861
## 1148 2016-02-22 2376.622 -599.45476 -564.0359246 1978.462
## 1149 2016-02-23 2377.473 -218.55228 -547.7683058 2376.482
## 1150 2016-02-24 2378.324 -213.16223 -530.8850731 2399.607
## 1151 2016-02-25 2379.175  -29.41662 -513.4796409 2601.608
## 1152 2016-02-26 2380.025  159.07673 -495.6586664 2808.773
## 1153 2016-02-27 2380.876  356.13985 -477.5392034 3024.807
## 1154 2016-02-28 2381.727  545.36929 -459.2455289 3233.180
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## 1156 2016-03-01 2383.428 -218.55228 -422.6482009 2507.558
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## 1158 2016-03-03 2385.130  -29.41662 -386.8735044 2734.169
## 1159 2016-03-04 2385.980  159.07673 -369.5829341 2940.804
## 1160 2016-03-05 2386.831  356.13985 -352.8214792 3155.479
## 1161 2016-03-06 2387.682  545.36929 -336.6685740 3361.713
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## 1164 2016-03-09 2390.234 -213.16223 -292.3765634 2650.025
## 1165 2016-03-10 2391.085  -29.41662 -279.0709974 2847.927
## 1166 2016-03-11 2391.936  159.07673 -266.4763529 3049.866
## 1167 2016-03-12 2392.786  356.13985 -254.5503347 3259.706
## 1168 2016-03-13 2393.637  545.36929 -243.2312236 3461.105
## 1169 2016-03-14 2394.251 -599.45476 -232.4396566 2327.687
## 1170 2016-03-15 2394.866 -218.55228 -222.0809040 2719.563
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## 1174 2016-03-19 2397.324  356.13985 -182.7023515 3336.091
## 1175 2016-03-20 2397.938  545.36929 -172.7556400 3535.882
## 1176 2016-03-21 2398.553 -599.45476 -162.5219279 2401.906
## 1177 2016-03-22 2399.167 -218.55228 -151.8881050 2794.056
## 1178 2016-03-23 2399.781 -213.16223 -140.7520530 2811.197
## 1179 2016-03-24 2400.396  -29.41662 -129.0255547 3007.284
## 1180 2016-03-25 2401.010  159.07673 -116.6368237 3208.780
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## 1183 2016-03-28 2402.854 -599.45476  -75.0659986 2493.663
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## 1186 2016-03-31 2404.697  -29.41662  -26.8631382 3113.747
## 1187 2016-04-01 2405.311  159.07673   -9.5134482 3320.204
## 1188 2016-04-02 2405.926  356.13985    8.3433204 3535.739
## 1189 2016-04-03 2406.540  545.36929   26.6018801 3743.841
## 1190 2016-04-04 2407.155 -599.45476   45.1437261 2618.173
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## 1193 2016-04-07 2408.998  -29.41662  101.1477045 3246.059
## 1194 2016-04-08 2409.612  159.07673  119.4784809 3453.497
## 1195 2016-04-09 2410.227  356.13985  137.4091142 3669.106
## 1196 2016-04-10 2410.841  545.36929  154.8076546 3876.348
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## 1199 2016-04-13 2412.685 -213.16223  202.6421547 3167.494
## 1200 2016-04-14 2413.299  -29.41662  216.8118908 3366.024
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## 1209 2016-04-23 2418.829  356.13985  297.8609289 3838.160
## 1210 2016-04-24 2419.443  545.36929  302.2832041 4032.426
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## 1214 2016-04-28 2421.901  -29.41662  314.8441533 3472.658
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## 1222 2016-05-06 2426.817  159.07673  338.4920809 3689.715
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## 1228 2016-05-12 2430.503  -29.41662  374.0621933 3540.479
## 1229 2016-05-13 2431.118  159.07673  381.8214940 3737.346
## 1230 2016-05-14 2431.732  356.13985  390.0282353 3943.230
## 1231 2016-05-15 2432.346  545.36929  398.6336798 4141.679
## 1232 2016-05-16 2432.961 -599.45476  407.5828192 3006.419
## 1233 2016-05-17 2433.575 -218.55228  416.8158801 3397.169
## 1234 2016-05-18 2434.190 -213.16223  426.2698273 3412.627
## 1235 2016-05-19 2434.804  -29.41662  435.8798290 3606.597
## 1236 2016-05-20 2435.419  159.07673  445.5806544 3805.406
## 1237 2016-05-21 2436.033  356.13985  455.3079774 4012.811
## 1238 2016-05-22 2436.647  545.36929  464.9995661 4212.346
## 1239 2016-05-23 2437.262 -599.45476  474.5963432 3077.733
## 1240 2016-05-24 2437.876 -218.55228  484.0433081 3468.697
## 1241 2016-05-25 2438.491 -213.16223  493.2903165 3483.949
## 1242 2016-05-26 2439.105  -29.41662  502.2927169 3677.311
## 1243 2016-05-27 2439.720  159.07673  511.0118509 3875.138
## 1244 2016-05-28 2440.334  356.13985  519.4154234 4081.219
## 1245 2016-05-29 2440.949  545.36929  527.4777556 4279.125
## 1246 2016-05-30 2441.563 -599.45476  535.1799327 3142.618
## 1247 2016-05-31 2442.177 -218.55228  542.5098596 3531.465
## 1248 2016-06-01 2442.792 -213.16223  549.4622400 3544.422
## 1249 2016-06-02 2443.406  -29.41662  556.0384906 3735.358
## 1250 2016-06-03 2444.021  159.07673  562.2466019 3930.674
## 1251 2016-06-04 2444.635  356.13985  568.1009558 4134.206
## 1252 2016-06-05 2445.250  545.36929  573.6221059 4329.571
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## 1255 2016-06-08 2447.093 -213.16223  588.4788997 3587.739
## 1256 2016-06-09 2447.707  -29.41662  592.9866387 3776.607
## 1257 2016-06-10 2448.322  159.07673  597.3464399 3970.075
## 1258 2016-06-11 2448.936  356.13985  601.6092808 4172.015
## 1259 2016-06-12 2449.551  545.36929  605.8296738 4366.079
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## 1263 2016-06-16 2452.008  -29.41662  623.4636788 3811.385
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## 1265 2016-06-18 2453.237  356.13985  633.5837522 4208.291
## 1266 2016-06-19 2453.852  545.36929  639.1768071 4403.728
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## 1269 2016-06-22 2455.695 -213.16223  658.6950051 3666.558
## 1270 2016-06-23 2456.309  -29.41662  666.2449874 3858.468
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## 1272 2016-06-25 2457.538  356.13985  683.0510671 4262.059
## 1273 2016-06-26 2458.153  545.36929  692.3141338 4461.166
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## 1276 2016-06-29 2459.996 -213.16223  723.2938029 3735.457
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## 1279 2016-07-02 2461.839  356.13985  757.8842866 4341.193
## 1280 2016-07-03 2462.454  545.36929  769.8027532 4542.956
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## 1282 2016-07-05 2463.683 -218.55228  793.4758048 3803.936
## 1283 2016-07-06 2464.297 -213.16223  804.9329147 3821.398
## 1284 2016-07-07 2464.912  -29.41662  815.9200952 4016.745
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## 1286 2016-07-09 2466.140  356.13985  835.7861299 4423.396
## 1287 2016-07-10 2466.755  545.36929  844.3056713 4621.760
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## 1290 2016-07-13 2468.598 -213.16223  862.0793220 3882.845
## 1291 2016-07-14 2469.213  -29.41662  864.8566050 4069.982
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## 1293 2016-07-16 2470.441  356.13985  864.8358948 4456.747
## 1294 2016-07-17 2471.056  545.36929  861.8192434 4643.574
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## 1298 2016-07-21 2473.514  -29.41662  828.3492141 4037.776
## 1299 2016-07-22 2474.128  159.07673  814.6334454 4213.168
## 1300 2016-07-23 2474.742  356.13985  798.8905583 4395.103
## 1301 2016-07-24 2475.357  545.36929  781.2329068 4567.289
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## 1305 2016-07-28 2477.815  -29.41662  694.7401707 3908.468
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## 1307 2016-07-30 2479.044  356.13985  644.9760831 4245.489
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## 1319 2016-08-11 2486.417  -29.41662  382.0665414 3604.397
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## 1419 2016-11-19 2547.860  356.13985   89.6048596 3758.935
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## 1461 2016-12-31 2573.667  356.13985 -842.3591924 2852.777
## 1462 2017-01-01 2574.281  545.36929 -843.8701017 3041.110
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## 1487 2017-01-26 2589.642  -29.41662 -818.0794581 2507.476
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## 1489 2017-01-28 2590.871  356.13985 -800.3725923 2911.968
## 1490 2017-01-29 2591.485  545.36929 -791.5128679 3110.671
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## 1497 2017-02-05 2595.786  545.36929 -734.0476629 3172.438
## 1498 2017-02-06 2596.401 -599.45476 -726.4764565 2035.799
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## 1501 2017-02-09 2598.244  -29.41662 -703.5537147 2630.603
## 1502 2017-02-10 2598.858  159.07673 -695.5426063 2827.722
## 1503 2017-02-11 2599.473  356.13985 -687.1842773 3033.758
## 1504 2017-02-12 2600.087  545.36929 -678.3816795 3232.405
## 1505 2017-02-13 2600.702 -599.45476 -669.0428402 2097.534
## 1506 2017-02-14 2601.316 -218.55228 -659.0842057 2489.009
## 1507 2017-02-15 2601.931 -213.16223 -648.4337167 2505.664
## 1508 2017-02-16 2602.545  -29.41662 -637.0335213 2701.425
## 1509 2017-02-17 2603.159  159.07673 -624.8422410 2902.724
## 1510 2017-02-18 2603.774  356.13985 -611.8367224 3113.407
## 1511 2017-02-19 2604.388  545.36929 -598.0132186 3317.074
## 1512 2017-02-20 2605.003 -599.45476 -583.3879687 2187.490
## 1513 2017-02-21 2605.617 -218.55228 -567.9971554 2584.398
## 1514 2017-02-22 2606.232 -213.16223 -551.8962456 2606.503
## 1515 2017-02-23 2606.846  -29.41662 -535.1587331 2807.601
## 1516 2017-02-24 2607.460  159.07673 -517.8743232 3013.993
## 1517 2017-02-25 2608.075  356.13985 -500.1466145 3229.398
## 1518 2017-02-26 2608.689  545.36929 -482.0903481 3437.298
## 1519 2017-02-27 2609.304 -599.45476 -463.8283069 2311.351
## 1520 2017-02-28 2609.918 -218.55228 -445.4879589 2711.208
## 1521 2017-03-01 2610.533 -213.16223 -427.1979430 2735.502
## 1522 2017-03-02 2611.147  -29.41662 -409.0845034 2937.976
## 1523 2017-03-03 2611.761  159.07673 -391.2679775 3144.900
## 1524 2017-03-04 2612.376  356.13985 -373.8594398 3359.986
## 1525 2017-03-05 2612.990  545.36929 -356.9576028 3566.732
## 1526 2017-03-06 2613.605 -599.45476 -340.6460618 2438.834
## 1527 2017-03-07 2614.219 -218.55228 -324.9909677 2836.006
## 1528 2017-03-08 2614.834 -213.16223 -310.0391919 2856.962
## 1529 2017-03-09 2615.448  -29.41662 -295.8170377 3055.544
## 1530 2017-03-10 2616.063  159.07673 -282.3295346 3258.140
## 1531 2017-03-11 2616.677  356.13985 -269.5603347 3468.586
## 1532 2017-03-12 2617.291  545.36929 -257.4722138 3670.518
## 1533 2017-03-13 2617.906 -599.45476 -246.0081622 2537.773
## 1534 2017-03-14 2618.520 -218.55228 -235.0930331 2930.205
## 1535 2017-03-15 2619.135 -213.16223 -224.6357000 2946.667
## 1536 2017-03-16 2619.749  -29.41662 -214.5316633 3141.131
## 1537 2017-03-17 2620.364  159.07673 -204.6660291 3340.104
## 1538 2017-03-18 2620.978  356.13985 -194.9167779 3547.531
## 1539 2017-03-19 2621.592  545.36929 -185.1582296 3747.133
## 1540 2017-03-20 2622.207 -599.45476 -175.2646091 2612.817
## 1541 2017-03-21 2622.821 -218.55228 -165.1136120 3004.485
## 1542 2017-03-22 2623.436 -213.16223 -154.5898721 3021.014
## 1543 2017-03-23 2624.050  -29.41662 -143.5882372 3216.375
## 1544 2017-03-24 2624.665  159.07673 -132.0167615 3417.054
## 1545 2017-03-25 2625.279  356.13985 -119.7993373 3626.949
## 1546 2017-03-26 2625.894  545.36929 -106.8778937 3829.715
## 1547 2017-03-27 2626.508 -599.45476  -93.2141072 2699.169
## 1548 2017-03-28 2627.122 -218.55228  -78.7905803 3095.109
## 1549 2017-03-29 2627.737 -213.16223  -63.6114599 3116.293
## 1550 2017-03-30 2628.351  -29.41662  -47.7024841 3316.562
## 1551 2017-03-31 2628.966  159.07673  -31.1104604 3522.262
## 1552 2017-04-01 2629.580  356.13985  -13.9021937 3737.148
## 1553 2017-04-02 2630.195  545.36929    3.8371007 3944.731
## 1554 2017-04-03 2630.809 -599.45476   22.0058532 2818.690
## 1555 2017-04-04 2631.423 -218.55228   40.4886046 3218.690
## 1556 2017-04-05 2632.038 -213.16223   59.1588111 3243.364
## 1557 2017-04-06 2632.652  -29.41662   77.8819095 3446.447
## 1558 2017-04-07 2633.267  159.07673   96.5185621 3654.192
## 1559 2017-04-08 2633.881  356.13985  114.9279911 3870.279
## 1560 2017-04-09 2634.496  545.36929  132.9713162 4078.166
## 1561 2017-04-10 2635.110 -599.45476  150.5148089 2951.500
## 1562 2017-04-11 2635.724 -218.55228  167.4329796 3349.935
## 1563 2017-04-12 2636.339 -213.16223  183.6114214 3372.118
## 1564 2017-04-13 2636.953  -29.41662  198.9493422 3571.816
## 1565 2017-04-14 2637.568  159.07673  213.3617255 3775.336
## 1566 2017-04-15 2638.182  356.13985  226.7810725 3986.433
## 1567 2017-04-16 2638.797  545.36929  239.1586893 4188.654
## 1568 2017-04-17 2639.411 -599.45476  250.4654973 3055.752
## 1569 2017-04-18 2640.026 -218.55228  260.6923567 3447.495
## 1570 2017-04-19 2640.640 -213.16223  269.8499068 3462.657
## 1571 2017-04-20 2641.254  -29.41662  277.9679392 3655.136
## 1572 2017-04-21 2641.869  159.07673  285.0943328 3851.370
## 1573 2017-04-22 2642.483  356.13985  291.2935882 4055.247
## 1574 2017-04-23 2643.098  545.36929  296.6450118 4250.442
## 1575 2017-04-24 2643.712 -599.45476  301.2406031 3110.828
## 1576 2017-04-25 2644.327 -218.55228  305.1827104 3496.287
## 1577 2017-04-26 2644.941 -213.16223  308.5815181 3505.690
## 1578 2017-04-27 2645.555  -29.41662  311.5524359 3693.021
## 1579 2017-04-28 2646.170  159.07673  314.2134574 3884.790
## 1580 2017-04-29 2646.784  356.13985  316.6825557 4084.937
## 1581 2017-04-30 2647.399  545.36929  319.0751773 4277.173
## 1582 2017-05-01 2648.013 -599.45476  321.5018946 3135.390
## 1583 2017-05-02 2648.628 -218.55228  324.0662671 3519.471
## 1584 2017-05-03 2649.242 -213.16223  326.8629546 3528.273
## 1585 2017-05-04 2649.856  -29.41662  329.9761189 3715.746
## 1586 2017-05-05 2650.471  159.07673  333.4781384 3908.356
## 1587 2017-05-06 2651.085  356.13985  337.4286525 4109.984
## 1588 2017-05-07 2651.700  545.36929  341.8739430 4304.273
## 1589 2017-05-08 2652.314 -599.45476  346.8466484 3165.036
## 1590 2017-05-09 2652.929 -218.55228  352.3658022 3552.072
## 1591 2017-05-10 2653.543 -213.16223  358.4371732 3564.148
## 1592 2017-05-11 2654.158  -29.41662  365.0538842 3755.125
## 1593 2017-05-12 2654.772  159.07673  372.1972753 3951.376
## 1594 2017-05-13 2655.386  356.13985  379.8379765 4156.694
## 1595 2017-05-14 2656.001  545.36929  387.9371491 4354.637
## 1596 2017-05-15 2656.615 -599.45476  396.4478554 3218.938
## 1597 2017-05-16 2657.230 -218.55228  405.3165146 3609.324
## 1598 2017-05-17 2657.844 -213.16223  414.4844027 3624.496
## 1599 2017-05-18 2658.459  -29.41662  423.8891606 3818.261
## 1600 2017-05-19 2659.073  159.07673  433.4662716 4016.946
## 1601 2017-05-20 2659.687  356.13985  443.1504782 4224.308
## 1602 2017-05-21 2660.302  545.36929  452.8771121 4423.878
## 1603 2017-05-22 2660.916 -599.45476  462.5833129 3289.375
## 1604 2017-05-23 2661.531 -218.55228  472.2091228 3680.517
## 1605 2017-05-24 2662.145 -213.16223  481.6984435 3696.011
## 1606 2017-05-25 2662.760  -29.41662  490.9998513 3889.673
## 1607 2017-05-26 2663.374  159.07673  500.0672693 4087.848
## 1608 2017-05-27 2663.988  356.13985  508.8605013 4294.319
## 1609 2017-05-28 2664.603  545.36929  517.3456332 4492.648
## 1610 2017-05-29 2665.217 -599.45476  525.4953146 3356.588
## 1611 2017-05-30 2665.832 -218.55228  533.2889310 3745.898
## 1612 2017-05-31 2666.446 -213.16223  540.7126815 3759.327
## 1613 2017-06-01 2667.061  -29.41662  547.7595760 3950.733
## 1614 2017-06-02 2667.675  159.07673  554.4293639 4146.511
## 1615 2017-06-03 2668.290  356.13985  560.7284079 4350.488
## 1616 2017-06-04 2668.904  545.36929  566.6695112 4546.273
## 1617 2017-06-05 2669.518 -599.45476  572.2717071 3407.665
## 1618 2017-06-06 2670.133 -218.55228  577.5600137 3794.470
## 1619 2017-06-07 2670.747 -213.16223  582.5651565 3805.480
## 1620 2017-06-08 2671.362  -29.41662  587.3232565 3994.598
## 1621 2017-06-09 2671.976  159.07673  591.8754788 4188.258
## 1622 2017-06-10 2672.591  356.13985  596.2676358 4390.328
## 1623 2017-06-11 2673.205  545.36929  600.5497344 4584.454
## 1624 2017-06-12 2673.819 -599.45476  604.7754578 3444.470
## 1625 2017-06-13 2674.434 -218.55228  609.0015708 3830.213
## 1626 2017-06-14 2675.048 -213.16223  613.2872366 3840.503
## 1627 2017-06-15 2675.663  -29.41662  617.6932390 4029.269
## 1628 2017-06-16 2676.277  159.07673  622.2810983 4222.965
## 1629 2017-06-17 2676.892  356.13985  627.1120812 4425.473
## 1630 2017-06-18 2677.506  545.36929  632.2461015 4620.451
## 1631 2017-06-19 2678.120 -599.45476  637.7405172 3481.736
## 1632 2017-06-20 2678.735 -218.55228  643.6488331 3869.161
## 1633 2017-06-21 2679.349 -213.16223  650.0193237 3881.536
## 1634 2017-06-22 2679.964  -29.41662  656.8935978 4072.771
## 1635 2017-06-23 2680.578  159.07673  664.3051292 4269.290
## 1636 2017-06-24 2681.193  356.13985  672.2777861 4474.940
## 1637 2017-06-25 2681.807  545.36929  680.8243947 4673.331
## 1638 2017-06-26 2682.422 -599.45476  689.9453766 3538.242
## 1639 2017-06-27 2683.036 -218.55228  699.6275032 3929.441
## 1640 2017-06-28 2683.650 -213.16223  709.8428108 3945.661
## 1641 2017-06-29 2684.265  -29.41662  720.5477218 4140.726
## 1642 2017-06-30 2684.879  159.07673  731.6824152 4340.968
## 1643 2017-07-01 2685.494  356.13985  743.1704878 4550.134
## 1644 2017-07-02 2686.108  545.36929  754.9189422 4751.726
## 1645 2017-07-03 2686.723 -599.45476  766.8185341 3619.416
## 1646 2017-07-04 2687.337 -218.55228  778.7445007 4012.859
## 1647 2017-07-05 2687.951 -213.16223  790.5576876 4030.677
## 1648 2017-07-06 2688.566  -29.41662  802.1060783 4226.585
## 1649 2017-07-07 2689.180  159.07673  813.2267228 4426.814
## 1650 2017-07-08 2689.795  356.13985  823.7480485 4635.013
## 1651 2017-07-09 2690.409  545.36929  833.4925259 4834.601
## 1652 2017-07-10 2691.024 -599.45476  842.2796515 3699.178
## 1653 2017-07-11 2691.638 -218.55228  849.9291960 4088.345
## 1654 2017-07-12 2692.252 -213.16223  856.2646596 4100.685
## 1655 2017-07-13 2692.867  -29.41662  861.1168634 4289.897
## 1656 2017-07-14 2693.481  159.07673  864.3276006 4482.216
## 1657 2017-07-15 2694.096  356.13985  865.7532632 4681.319
## 1658 2017-07-16 2694.710  545.36929  865.2683579 4870.678
## 1659 2017-07-17 2695.325 -599.45476  862.7688204 3723.969
## 1660 2017-07-18 2695.939 -218.55228  858.1750400 4100.892
## 1661 2017-07-19 2696.554 -213.16223  851.4345087 4100.156
## 1662 2017-07-20 2697.168  -29.41662  842.5240123 4275.605
## 1663 2017-07-21 2697.782  159.07673  831.4512933 4453.640
## 1664 2017-07-22 2698.397  356.13985  818.2561207 4638.123
## 1665 2017-07-23 2699.011  545.36929  803.0107173 4812.721
## 1666 2017-07-24 2699.626 -599.45476  785.8195079 3651.320
## 1667 2017-07-25 2700.240 -218.55228  766.8181677 4013.836
## 1668 2017-07-26 2700.855 -213.16223  746.1719679 3999.194
## 1669 2017-07-27 2701.469  -29.41662  724.0734309 4161.456
## 1670 2017-07-28 2702.083  159.07673  700.7393282 4327.229
## 1671 2017-07-29 2702.698  356.13985  676.4070697 4500.575
## 1672 2017-07-30 2703.312  545.36929  651.3305503 4665.342
## 1673 2017-07-31 2703.927 -599.45476  625.7755367 3495.577
## 1674 2017-08-01 2704.541 -218.55228  600.0146899 3851.333
## 1675 2017-08-02 2705.156 -213.16223  574.3223318 3831.646
## 1676 2017-08-03 2705.770  -29.41662  548.9690725 3990.652
## 1677 2017-08-04 2706.385  159.07673  524.2164240 4155.008
## 1678 2017-08-05 2706.999  356.13985  500.3115270 4328.780
## 1679 2017-08-06 2707.613  545.36929  477.4821187 4495.795
## 1680 2017-08-07 2708.228 -599.45476  455.9318676 3330.035
## 1681 2017-08-08 2708.842 -218.55228  435.8361925 3691.456
## 1682 2017-08-09 2709.457 -213.16223  417.3386752 3678.963
## 1683 2017-08-10 2710.071  -29.41662  400.5481633 3846.533
## 1684 2017-08-11 2710.686  159.07673  385.5366421 4020.629
## 1685 2017-08-12 2711.300  356.13985  372.3379391 4205.108
## 1686 2017-08-13 2711.914  545.36929  360.9473034 4383.561
## 1687 2017-08-14 2712.529 -599.45476  351.3218793 3229.726
## 1688 2017-08-15 2713.143 -218.55228  343.3820730 3603.303
## 1689 2017-08-16 2713.758 -213.16223  337.0137879 3602.939
## 1690 2017-08-17 2714.372  -29.41662  332.0714798 3782.357
## 1691 2017-08-18 2714.987  159.07673  328.3819633 3967.775
## 1692 2017-08-19 2715.601  356.13985  325.7488793 4162.820
## 1693 2017-08-20 2716.215  545.36929  323.9577162 4350.872
## 1694 2017-08-21 2716.830 -599.45476  322.7812601 3205.486
## 1695 2017-08-22 2717.444 -218.55228  321.9853385 3586.207
## 1696 2017-08-23 2718.059 -213.16223  321.3347113 3591.561
## 1697 2017-08-24 2718.673  -29.41662  320.5989596 3775.185
## 1698 2017-08-25 2719.288  159.07673  319.5582181 3963.252
## 1699 2017-08-26 2719.902  356.13985  318.0086034 4159.380
## 1700 2017-08-27 2720.517  545.36929  315.7671938 4346.983
## 1701 2017-08-28 2721.131 -599.45476  312.6764304 3199.682
## 1702 2017-08-29 2721.745 -218.55228  308.6078192 3577.131
## 1703 2017-08-30 2722.360 -213.16223  303.4648366 3577.992
## 1704 2017-08-31 2722.974  -29.41662  297.1849578 3756.072
## 1705 2017-09-01 2723.589  159.07673  289.7407524 3937.736
## 1706 2017-09-02 2724.203  356.13985  281.1400156 4126.813
## 1707 2017-09-03 2724.818  545.36929  271.4249298 4306.942
## 1708 2017-09-04 2725.432 -599.45476  260.6702789 3151.977
## 1709 2017-09-05 2726.046 -218.55228  248.9807609 3521.805
## 1710 2017-09-06 2726.661 -213.16223  236.4874738 3515.316
## 1711 2017-09-07 2727.275  -29.41662  223.3436686 3686.532
## 1712 2017-09-08 2727.890  159.07673  209.7198888 3862.016
## 1713 2017-09-09 2728.504  356.13985  195.7986300 4045.773
## 1714 2017-09-10 2729.119  545.36929  181.7686703 4221.586
## 1715 2017-09-11 2729.733 -599.45476  167.8192322 3063.427
## 1716 2017-09-12 2730.347 -218.55228  154.1341415 3431.259
## 1717 2017-09-13 2730.962 -213.16223  140.8861523 3424.016
## 1718 2017-09-14 2731.576  -29.41662  128.2316030 3595.721
## 1719 2017-09-15 2732.191  159.07673  116.3055604 3772.903
## 1720 2017-09-16 2732.805  356.13985  105.2175979 3959.493
## 1721 2017-09-17 2733.420  545.36929   95.0483363 4139.167
## 1722 2017-09-18 2734.034 -599.45476   85.8468555 2985.756
## 1723 2017-09-19 2734.649 -218.55228   77.6290634 3359.055
## 1724 2017-09-20 2735.263 -213.16223   70.3770796 3357.808
## 1725 2017-09-21 2735.877  -29.41662   64.0396660 3535.830
## 1726 2017-09-22 2736.492  159.07673   58.5337048 3719.432
## 1727 2017-09-23 2737.106  356.13985   53.7466955 3912.323
## 1728 2017-09-24 2737.721  545.36929   49.5402136 4097.960
## 1729 2017-09-25 2738.335 -599.45476   45.7542432 2949.964
## 1730 2017-09-26 2738.950 -218.55228   42.2122725 3327.939
## 1731 2017-09-27 2739.564 -213.16223   38.7270145 3330.459
## 1732 2017-09-28 2740.178  -29.41662   35.1065980 3511.198
## 1733 2017-09-29 2740.793  159.07673   31.1610554 3696.361
## 1734 2017-09-30 2741.407  356.13985   26.7089238 3889.586
## 1735 2017-10-01 2742.022  545.36929   21.5837696 4074.305
## 1736 2017-10-02 2742.636 -599.45476   15.6404434 2924.152
## 1737 2017-10-03 2743.251 -218.55228    8.7608790 3298.789
## 1738 2017-10-04 2743.865 -213.16223    0.8592559 3296.892
## 1739 2017-10-05 2744.479  -29.41662   -8.1136378 3472.279
## 1740 2017-10-06 2745.094  159.07673  -18.1669883 3651.334
## 1741 2017-10-07 2745.708  356.13985  -29.2676077 3837.910
## 1742 2017-10-08 2746.323  545.36929  -41.3387481 4015.683
## 1743 2017-10-09 2746.937 -599.45476  -54.2601449 2858.552
## 1744 2017-10-10 2747.552 -218.55228  -67.8693208 3226.460
## 1745 2017-10-11 2748.166 -213.16223  -81.9641511 3218.370
## 1746 2017-10-12 2748.781  -29.41662  -96.3066533 3388.387
## 1747 2017-10-13 2749.395  159.07673 -110.6279327 3563.174
## 1748 2017-10-14 2750.009  356.13985 -124.6341826 3746.845
## 1749 2017-10-15 2750.624  545.36929 -138.0136052 3923.309
## 1750 2017-10-16 2751.238 -599.45476 -150.4440953 2766.669
## 1751 2017-10-17 2751.853 -218.55228 -161.6015022 3137.029
## 1752 2017-10-18 2752.467 -213.16223 -171.1682680 3133.467
## 1753 2017-10-19 2753.082  -29.41662 -178.8422250 3310.153
## 1754 2017-10-20 2753.696  159.07673 -184.3453285 3493.757
## 1755 2017-10-21 2754.310  356.13985 -187.4320959 3688.348
## 1756 2017-10-22 2754.925  545.36929 -187.8975279 3877.727
## 1757 2017-10-23 2755.539 -599.45476 -185.5842965 2735.830
## 1758 2017-10-24 2756.154 -218.55228 -180.3889986 3122.542
## 1759 2017-10-25 2756.768 -213.16223 -172.2672942 3136.669
## 1760 2017-10-26 2757.383  -29.41662 -161.2377753 3332.058
## 1761 2017-10-27 2757.997  159.07673 -147.3844381 3535.019
## 1762 2017-10-28 2758.611  356.13985 -130.8576659 3749.224
## 1763 2017-10-29 2759.226  545.36929 -111.8736672 3958.051
## 1764 2017-10-30 2759.840 -599.45476  -90.7123481 2835.003
## 1765 2017-10-31 2760.455 -218.55228  -67.7136403 3239.519
## 1766 2017-11-01 2761.069 -213.16223  -43.2723417 3269.965
## 1767 2017-11-02 2761.684  -29.41662  -17.8315668 3479.765
## 1768 2017-11-03 2762.298  159.07673    8.1250629 3694.830
## 1769 2017-11-04 2762.913  356.13985   34.0823238 3918.465
## 1770 2017-11-05 2763.527  545.36929   59.5031979 4133.729
## 1771 2017-11-06 2764.141 -599.45476   83.8393661 3013.856
## 1772 2017-11-07 2764.756 -218.55228  106.5421522 3418.076
## 1773 2017-11-08 2765.370 -213.16223  127.0736677 3444.612
## 1774 2017-11-09 2765.985  -29.41662  144.9179027 3646.816
## 1775 2017-11-10 2766.599  159.07673  159.5915046 3850.597
## 1776 2017-11-11 2767.214  356.13985  170.6539952 4059.337
## 1777 2017-11-12 2767.828  545.36929  177.7171863 4256.244
## 1778 2017-11-13 2768.442 -599.45476  180.4535726 3114.771
## 1779 2017-11-14 2769.057 -218.55228  178.6035043 3494.438
## 1780 2017-11-15 2769.671 -213.16223  171.9809685 3493.820
## 1781 2017-11-16 2770.286  -29.41662  160.4778450 3666.677
## 1782 2017-11-17 2770.900  159.07673  144.0665325 3839.373
## 1783 2017-11-18 2771.515  356.13985  122.8008841 4015.785
## 1784 2017-11-19 2772.129  545.36929   96.8154296 4179.644
## 1785 2017-11-20 2772.744 -599.45476   66.3229012 3004.942
## 1786 2017-11-21 2773.358 -218.55228   31.6101225 3351.746
## 1787 2017-11-22 2773.972 -213.16223   -6.9676448 3319.172
## 1788 2017-11-23 2774.587  -29.41662  -48.9937624 3461.506
## 1789 2017-11-24 2775.201  159.07673  -93.9985201 3605.609
## 1790 2017-11-25 2775.816  356.13985 -141.4684913 3755.817
## 1791 2017-11-26 2776.430  545.36929 -190.8567189 3896.273
## 1792 2017-11-27 2777.045 -599.45476 -241.5934994 2701.326
## 1793 2017-11-28 2777.659 -218.55228 -293.0975145 3031.339
## 1794 2017-11-29 2778.273 -213.16223 -344.7870572 2985.654
## 1795 2017-11-30 2778.888  -29.41662 -396.0910985 3118.710
## 1796 2017-12-01 2779.502  159.07673 -446.4599468 3257.449
## 1797 2017-12-02 2780.117  356.13985 -495.3752643 3406.211
## 1798 2017-12-03 2780.731  545.36929 -542.3592240 3549.071
## 1799 2017-12-04 2781.346 -599.45476 -586.9826125 2360.238
## 1800 2017-12-05 2781.960 -218.55228 -628.8717129 2699.866
## 1801 2017-12-06 2782.574 -213.16223 -667.7138328 2667.028
## 1802 2017-12-07 2783.189  -29.41662 -703.2613766 2815.841
## 1803 2017-12-08 2783.803  159.07673 -735.3343990 2972.876
## 1804 2017-12-09 2784.418  356.13985 -763.8216135 3142.066
## 1805 2017-12-10 2785.032  545.36929 -788.6798665 3307.051
## 1806 2017-12-11 2785.647 -599.45476 -809.9321264 2141.590
## 1807 2017-12-12 2786.261 -218.55228 -827.6640702 2505.375
## 1808 2017-12-13 2786.876 -213.16223 -842.0193845 2497.024
## 1809 2017-12-14 2787.490  -29.41662 -853.1939243 2670.209
## 1810 2017-12-15 2788.104  159.07673 -861.4289009 2851.082
## 1811 2017-12-16 2788.719  356.13985 -867.0032873 3043.185
## 1812 2017-12-17 2789.333  545.36929 -870.2256469 3229.807
## 1813 2017-12-18 2789.948 -599.45476 -871.4255986 2084.397
## 1814 2017-12-19 2790.562 -218.55228 -870.9451377 2466.395
## 1815 2017-12-20 2791.177 -213.16223 -869.1300271 2474.214
## 1816 2017-12-21 2791.791  -29.41662 -866.3214695 2661.383
## 1817 2017-12-22 2792.405  159.07673 -862.8482552 2853.964
## 1818 2017-12-23 2793.020  356.13985 -859.0195659 3055.470
## 1819 2017-12-24 2793.634  545.36929 -855.1185906 3249.215
## 1820 2017-12-25 2794.249 -599.45476 -851.3970873 2108.727
## 1821 2017-12-26 2794.863 -218.55228 -848.0709926 2493.570
## 1822 2017-12-27 2795.478 -213.16223 -845.3171553 2502.328
## 1823 2017-12-28 2796.092  -29.41662 -843.2712341 2688.734
## 1824 2017-12-29 2796.706  159.07673 -842.0267730 2879.086
## 1825 2017-12-30 2797.321  356.13985 -841.6354302 3077.155
## 1826 2017-12-31 2797.935  545.36929 -842.1083139 3266.526

Model fine Tuning untuk melihat trend liner dari permintaan

Ini digunakan untuk melihat trend perkiraan dengan bentuk lain yaitu dengan menambahkan changepoint

plot(model_ts, forecast_ts) + 
  add_changepoints_to_plot(model_ts, threshold = 0) 

Garis merah putus-putus menunjukkan change point dari trend

before_2017 <- daily_demandstore03 %>% 
  mutate( 
    year = year(date) 
  ) %>% 
  filter(year < 2017) %>% 
  rename( 
    ds = "date", 
    y = "demand" 
  ) 

after_2017 <- daily_demandstore03 %>% 
  mutate( 
    year = year(date) 
  ) %>% 
  filter(year >= 2017) %>% 
  rename( 
    ds = "date", 
    y = "demand" 
  ) 
ggplot(before_2017, aes(x=ds, y=y)) + 
  geom_point() + 
  theme_minimal()

# Model sebelum 2017 dan visualisasinya
model_before_2017 <- prophet(yearly.seasonality = TRUE, 
                             changepoint.prior.scale = 0.01) %>% 
  fit.prophet(before_2017) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_before_2017 <- make_future_dataframe(model_before_2017, periods = 365) 
forecaset_before_2017 <- predict(model_before_2017, future_before_2017) 
plot(model_before_2017, forecaset_before_2017) + 
  add_changepoints_to_plot(model_before_2017) + 
  geom_point(data = after_2017, aes(x = as.POSIXct(ds), y=y), color = "tomato3")

# Melihat transaksi paling banyak dalam satu minggu
forecast_ts %>% 
  mutate( 
    weekday = wday(ds, label = TRUE), 
    weekly = round(weekly, 5) 
  ) %>% 
  filter(ds <= max(daily_demandstore03$date)) %>% 
  select(weekday, weekly) %>% 
  distinct() %>% 
  arrange(-weekly)

## Warning: There was 1 warning in `filter()`.
## ℹ In argument: `ds <= max(daily_demandstore03$date)`.
## Caused by warning in `check_tzones()`:
## ! 'tzone' attributes are inconsistent

##   weekday     weekly
## 1     Sun  545.36929
## 2     Sat  356.13985
## 3     Fri  159.07673
## 4     Thu  -29.41662
## 5     Wed -213.16223
## 6     Tue -218.55228
## 7     Mon -599.45476

# Visualisasi Model Sebelum Tahun 2017 berdasarkan hari dalam satu minggu
daily_demandstore03 %>% 
  mutate( 
    wday = wday(date, label = TRUE) 
  ) %>% 
  ggplot(aes(x=date, y=demand)) + 
  geom_point(aes(color=wday)) 

Berdasarkan visualisasi diatas dapat disumpulan bahwa penjualan tertinggi pada tiap tahun ada pada hari Jumat, Sabtu dan Minggu

Model Evalution

Untuk melakukan evaluasi dari model yang sudah disiapkan, maka kita bisa menguji model tersebut pada data testing.

# Menyiapkan data
test <- read.csv("data/test.csv")
glimpse(test)

## Rows: 182,500
## Columns: 4
## $ date  <chr> "2017-01-01", "2017-01-02", "2017-01-03", "2017-01-04", "2017-01…
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ item  <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ sales <int> 19, 15, 10, 16, 14, 24, 14, 20, 18, 11, 14, 17, 7, 16, 29, 15, 1…

ada 182500 baris dan 4 kolom untuk data testing

# Merubah type data tanggal menjadi date
test %>% 
  mutate (date = as.Date(date)) %>%
  group_by(date) %>% 
  summarise( 
    demand=sum(sales)
  )

## # A tibble: 365 × 2
##    date       demand
##    <date>      <int>
##  1 2017-01-01  23709
##  2 2017-01-02  15772
##  3 2017-01-03  18650
##  4 2017-01-04  18510
##  5 2017-01-05  19895
##  6 2017-01-06  20994
##  7 2017-01-07  22591
##  8 2017-01-08  23700
##  9 2017-01-09  15797
## 10 2017-01-10  18608
## # ℹ 355 more rows

Bisa dilihat bahwa semua data testing ada pada tahun 2017.

Kita akan bandingkan data set Test dengan data set Training utk data sebelum tahun 2018, karena data train hanya sampai akhir 2016

cutoff <- dmy("01-01-2016") 
train <- daily_demandstore03 %>% 
  filter( 
    date < cutoff 
  ) %>% 
  rename( 
    "ds" = date, 
    "y" = demand 
  ) 
test <- daily_demandstore03 %>% 
  filter( 
    date >= cutoff 
  ) %>% 
  rename( 
    "ds" = date, 
    "y" = demand 
  ) 
ggplot(daily_demandstore03, aes(x=date, y=demand)) + 
  geom_point(data = train, aes(x=ds, y=y)) + 
  geom_point(data = test, aes(x=ds, y=y), color="tomato3")

Warna hitam adalah data training dan warna merah adalah data testing

Model Final

Model final digunakan untuk mempredisi data testing

# Menyiapkan model final
model_final <- prophet(changepoint.prior.scale = 0.05, 
                       yearly.seasonality = TRUE, 
                       holidays = holiday) %>% 
  add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>% 
  fit.prophet(train) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_final <- make_future_dataframe(model_final, periods = nrow(test) + 1) 
forecast_final <- predict(model_final, future_final) 
plot(model_final, forecast_final)

Visual Model Final dengan data testing

plot(model_final, forecast_final) + 
  geom_point(data = test %>% 
               mutate(ds = as.POSIXct(ds)), aes(x=ds, y=y), color="tomato3")

Bisa dilihat bahwa model dapat memprediksi data testing dan sama dengan trend yang sudah diperkirakan sebelumnya.

Menghitung Akurasi dari Model

Untuk menentukan tingkat akurasi model, biasanya menghitung terlebih dulu nilai MAPE dari model. MAPE adalah Mean Absolute Persentase Error biasanya digunakan mengavaluasi model deret waktu.

eval <- test %>% 
  mutate( 
    ds = as.POSIXct(ds) 
  ) %>% 
  left_join(forecast_final) %>% 
  select(ds, y, yhat, yhat_upper, yhat_lower) 

## Joining with `by = join_by(ds)`

eval 

## # A tibble: 366 × 5
##    ds                      y  yhat yhat_upper yhat_lower
##    <dttm>              <int> <dbl>      <dbl>      <dbl>
##  1 2016-01-01 00:00:00  2284 2416.      2571.      2253.
##  2 2016-01-02 00:00:00  2384 2616.      2778.      2455.
##  3 2016-01-03 00:00:00  2590 2795.      2955.      2636.
##  4 2016-01-04 00:00:00  1714 1685.      1843.      1526.
##  5 2016-01-05 00:00:00  2004 2046.      2200.      1885.
##  6 2016-01-06 00:00:00  2060 2044.      2203.      1891.
##  7 2016-01-07 00:00:00  2168 2224.      2384.      2056.
##  8 2016-01-08 00:00:00  2343 2398.      2561.      2249.
##  9 2016-01-09 00:00:00  2443 2590.      2749.      2427.
## 10 2016-01-10 00:00:00  2618 2765.      2928.      2604.
## # ℹ 356 more rows

Untuk mendapatkan nilai mape kita harus mengurangi nilai sebenarnya dengan nilai yang ada pada data testing (yhat) yang ada dalam data frame forecast_final

mape <- function(y, yhat) { 
  return(mean(abs(y - yhat)/ y)) 
} 
mape(eval$y, eval$yhat)

## [1] 0.0441405

Bisa dilihat bahwa nilai MAPE dari model adalah 0.04, sehingga akurasi dari model adalah 0,96 (96%). Jadi bisa disimpulkan bahwa model sangat akurat dalam melakukan prediksi.